It’s looking more and more like Jack Dorsey is going to have two CEO jobs for the foreseeable future.

Dorsey — who is the CEO of Square as well as the interim CEO of Twitter — has been telling insiders involved in the high-profile payments company’s current IPO process that he will not leave the top management role at Square, according to three sources familiar with the situation. That includes bankers, legal advisers and key execs. Dorsey is also prepared to tell public market investors that are interested in investing in Square once it begins the active part of its IPO process the same thing, even if he is also named permanent CEO of Twitter.

Dorsey has twice issued public statements stating as much, on the day Twitter named him interim CEO and again when Re/code requested a comment for a story on possible replacements for him at Square.

But things got murky — perhaps bizarre is a better word — when Twitter’s board of directors issued a thinly veiled ultimatum, stating that the Twitter CEO job was a full-time gig. Translation: Give up the Square CEO role, Jack, if you want to keep the top Twitter job.

Right now, though, that demand looks to have fallen very flat, largely because the leverage appears to now rest mostly with Dorsey, who is the top choice for the Twitter CEO job for several board members, according to sources. The question now is if and how its directors can walk back the board’s previous statement if it indeed chooses Dorsey and he remains adamant about keeping his post at Square.

The other obvious question is whether Dorsey is capable of doing both jobs permanently. While the idea of running two public companies sounds initially absurd on the surface, there are plenty of people in and around each company who think Dorsey could make it work.

One big reason: Dorsey has hired a widely respected — and deep — management team at Square and can also lean on strong senior leaders at Twitter, including star revenue boss Adam Bain. And one of the small reasons, which sure seems trivial but which supporters insist is not: Twitter and Square headquarters sit just one block apart on Market Street in San Francisco.

Spokesmen for Square and Twitter declined to comment.

Additional reporting by Kara Swisher.