News flash for Twitter's board: Jack Dorsey is not going to give up the Square CEO job

If Twitter wants Jack Dorsey as CEO, the company is going to have to share him.

That's because Dorsey has apparently made it clear he has no intention of giving up his job as CEO of digital payments company Square.

According to a report in Recode, Dorsey has been telling insiders involved in Square's upcoming IPO that he will not step down from the job. And he intends to say the same thing publicly once the Square IPO roadshow gets underway.

This matches statements we heard earlier this summer from two people close to Square who said they could not imagine Dorsey stepping down, and that there was nobody on Square's bench who could easily take his place.

Dorsey is currently "interim" CEO and is considered a front-runner for the Twitter gig. But Twitter's board said in June that it would only consider CEO candidates who were able to make a "full-time commitment," which would seemingly force Dorsey to make a choice.

According to Recode, the full-time commitment demand "appears to have fallen flat." Dorsey is the top choice of several board members for the job and he has all the leverage, Recode says.

Twitter has been searching for a full-time CEO since Dick Costolo resigned in June. Now they may need a face-saving way to scrap its previous statement, if indeed it wants to give Dorsey the job.

Meanwhile, investors are increasingly clamoring for the company to make a decision so that it can focus on revamping its business. And shares of Twitter remain down more than 25% since before Costolo resigned.