NEW YORK (TheStreet) -- The Twitter (TWTR) board is not pressuring Twitter and Square (SQ) CEO Jack Dorsey to choose a sole company to run instead of splitting his time between the two, sources told CNBC's Scott Wapner. 

The board still fully supports Dorsey because he is a "product person," Wapner reported on CNBC's "Halftime Report" on Friday afternoon. Dorsey is currently focused on improving the user experience on the struggling social media platform. 

LMM (LM) Chief Investment Officer Bill Miller said Dorsey needs to pick a company to run during a guest appearance on CNBC's "Closing Bell" last month. 

"It is insane to have Jack Dorsey be a part-time CEO at a company with the issues that Twitter has," Miller said. "I mean if a part-time CEO makes sense then so does a part-time CFO, part-time chief technology officer," he argued.

Others have voiced the same opinion, Wapner noted. "Do you want him to choose?" he asked Ritholtz Wealth Management CEO Josh Brown on today's show. 

"No, I don't really care that much. I would rather have a portion of him, quite frankly, than somebody coming from somewhere else and taking a year to figure this whole thing out all over again and probably not being able to," Brown answered. 

Brown believes that Dorsey has enough pressure on him without the added pressure from Twitter's board.

Putting someone else in the CEO role of Twitter wouldn't help it, Najarian Family Office co-founder Jon Najarian said in agreement. "If you put somebody else in this spot, they're in the captain's chair on the same ship."

Shareholders may be upset because Twitter's performance hasn't been great lately, but that could change, Brown noted. 

"We're very, very, very much tied to what have you done for me lately? He hasn't done much for investors lately. That could change on a dime," he explained. 

Shares of Twitter were higher in early afternoon trading on Friday. 

Separately, TheStreet Ratings objectively rated this stock according to its "risk-adjusted" total return prospect over a 12-month investment horizon. Not based on the news in any given day, the rating may differ from Jim Cramer's view or that of this articles's author.

TheStreet Ratings team rates Twitter as a Hold with a ratings score of C-. The primary factors that have impacted the team's rating are mixed - some indicating strength, some showing weaknesses, with little evidence to justify the expectation of either a positive or negative performance for this stock relative to most other stocks.

You can view the full analysis from the report here: TWTR

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