Overstock.com ( OSTK) CEO Patrick Byrne apparently has another variable to deal with amid the company's short-selling controversy -- his father.

According to the online edition of The Wall Street Journal, Byrne's father, company Chairman Jack Byrne, says he is mulling stepping down from his post at the online retailer.

The Journal reported the elder Byrne saying that one thing that may cause him to leave is the disagreement with his son on a public squabble with short sellers and analysts who are alleged to have been conspiring to damage Overstock shares.

"After the shareholder meeting in April this year, I'm going to give some serious consideration of whether I'm going to stay as chairman of the board," the elder Byrne told the Journal. "Patrick and I have had some wonderful times together on Overstock, but we've also had some stormy times. I'd rather keep my relationship with my son than be the chairman of the board of another company."

Last August, Byrne filed a lawsuit against Rocker Partners, a New Jersey hedge fund that specializes in short-selling, and Gradient Analytics, an independent research firm based in Scottsdale, Ariz. The lawsuit alleged that Rocker and Gradient worked together in publishing negative research on Overstock.com.

Rocker is a minority shareholder in TheStreet.com ( TSCM).

Subsequently, the Securities and Exchange Commission began an investigation into the allegations surrounding Gradient and Rocker. As part of the probe, TheStreet.com and its co-founder and major shareholder were served subpoenas .

Last Friday, Dow Jones ( DJ) confirmed that two of its reporters had received SEC subpoenas.

TheStreet.com, Cramer and Dow Jones have objected to the government's demands. The actions sparked controversy, and on Monday, SEC Chairman Christopher Cox sought to distance himself from the unusual investigative move.

But the happenings appear to be weighing heavily on the elder Byrne -- and his concern about the resulting distraction. Earlier Thursday, the Globe and Mail of Toronto quoted the elder Byrne as saying: "There may be something to this, I don't know whether there is or there isn't. I wish he would just pay attention to just running his company. That's the problem with the world today, sons don't do what their fathers tell them to do."