The newest game on Wall Street is betting on which big bank executive will lose his job first:

Citigroup

(C) - Get Report

Chairman and Chief Executive Sanford Weill or

J.P. Morgan Chase

(JPM) - Get Report

Chairman and Chief Executive William Harrison.

Until recently, the odds favored Harrison, what with J.P. Morgan's endless tide of bad telecom loans, its floundering investment bank and its inability to produce anything but anemic profit for the past few quarters. Indeed, on Tuesday, David Hendler, a financial-services analyst with independent research firm CreditSights, predicted that Harrison will be shoved overboard by year's end and replaced by David Coulter, the chief of J.P. Morgan's investment-banking division.

But speculation is mounting on Wall Street that the 69-year-old Weill may beat Harrison to the door -- either by choice or under pressure from securities regulators and possibly Citigroup's board. "Weill's case is looking weaker," said Hendler, who thinks Weill may find himself out on the street sometime next year.

The swift departure of both executives could provide a badly needed lift to the stocks of both banks, some analysts say, since the banks have been weighed down by a myriad of scandals.

Sparking the Weill-watch speculation is all the bad publicity Citigroup is getting over the allegations that Weill may have prodded Jack Grubman, Salomon's former star telecom analyst, to issue a more favorable rating on shares of

AT&T

(T) - Get Report

, as part of a bizarre deal to help get Grubman's twins admitted to an elite New York nursery school.

The "nursery-gate" allegations came to light last week in a series of emails written by Grubman to a female friend, which were uncovered by investigators for New York Attorney General Eliot Spitzer. The episode forced Weill to acknowledge that he not only made a telephone call to the nursery school on Grubman's behalf, but Citigroup made a $1 million donation to the school around the time Grubman's children were seeking admission.

While the legal experts say it's doubtful Spitzer has enough evidence to file either civil or criminal charges against Weill, the revelations are embarrassing nonetheless and put another dent in Weill's reputation as the consummate Wall Street wheeler-dealer.

The allegations are especially damaging because they come at the end of a year in which Citigroup has been pilloried in the press and by regulators and lawmakers for some of its business dealings with failed corporate giants like

Enron

and

WorldCom

. The assorted scandals have helped erase $55 billion in market capitalization from Citigroup's stock, even though the financial-services giant remains a money-making machine -- generating nearly $11 billion in net profit so far this year.

Several Wall Street money managers and analysts even suggest Spitzer could demand that Weill announce he's stepping down from Citigroup, as part of a settlement of a nearly yearlong investigation into business practices of Citi's Salomon Smith Barney investment bank.

"It's something that has to be considered, that he could be replaced," said Sean Egan, president of Egan-Jones Ratings, a small corporate rating service. "Spitzer may make it too expensive for Citigroup to keep him."

It's believed that as part of any settlement, Spitzer is going to demand that Citigroup pay a stiff fine, possibly as much as $200 million.

One money manager, who didn't want to be identified and doesn't own any Citigroup shares, said Weill's resignation could be the "trophy" that Spitzer has been looking for in his quest to portray himself as the one public official willing to take on Wall Street and defend the interests of ordinary investors.

A source familiar with the investigation said that over the past few weeks, Spitzer met with several Citigroup board members to brief them on his investigation.

A spokesman for Spitzer's office was unavailable for comment, and a spokeswoman for Citigroup declined to comment.

While lawyers say it's unlikely that Weill would agree to a deal that would force him to step down, it's not unprecedented for prosecutors and regulators to make such a demand in settling high-profile investigations.

"It wouldn't surprise me if this was something on the attorney general's table," said Jonathan Kord Lagemann, a New York securities lawyer and former general counsel for a small brokerage firm. "But I don't think Sandy Weill will agree to that."

Weill's supporters note that Citigroup this year has taken a number of steps to eliminate the problems regulators are looking into. Citigroup, for instance, announced earlier this month a more formal separation between its investment banking division and retail brokerage outfit. Critics, however, point out that Weill and Citigroup are enacting those reforms because of all the regulatory heat they are facing.

But even if Weill doesn't step down as part a deal with Spitzer, the sentiment on Wall Street is that his departure from Citigroup is only a matter of time and the bank's board will soon begin the long overdue process of selecting a successor.

And if Weill and Harrison both depart in the next few months, many say it actually could be a good thing for investors.

Hendler says a top-level management shakeup at J.P. Morgan probably would help boost the bank's ailing stock because Wall Street would see it as a sign the nation's second-largest bank is trying to get its financial affairs in order.

Similarly, Stephen Biggar, a bank analyst with Standard & Poor's, said he doubts Weill's departure would have much of a negative impact on the bank's stock. With the stock down trading 33% below its 52-week high, Biggar said, "any Weill premium in the stock has been long since removed."

Indeed, money managers say Citigroup's reputation as a moneymaking enterprise probably won't skip a beat with Weill out of the picture.

"Citi was a well-run organization before Weill showed up," said Michael Stead, a portfolio manager with Wells Capital Management's SIFE financial services fund, an $800 million fund that invests heavily in Citigroup shares. "The cemetery is full of lots of irreplaceable people."