Stoudamire, who would like to decide Wednesday where he'll spend the rest of the season, was expected to speak by telephone Tuesday with San Antonio Spurs coach Gregg Popovich and Phoenix Suns coach Mike D'Antoni, a source close to the situation told ESPN.com.
The Toronto Raptors also remained in the picture, the source said.
Although Stoudamire would seem to be the perfect fit for a Boston team needing an experienced playmaker behind second-year point guard Rajon Rondo, Celtics president Danny Ainge has expressed misgivings about tinkering with his team's chemistry.
Stoudamire has apparently taken that as a signal that the Celtics are not as interested in him as he had believed just a few days ago.
In San Antonio, Stoudamire would supplant Jacque Vaughn as a backup behind Tony Parker. In Phoenix, he would play behind Steve Nash and allow the Suns to move Leandro Barbosa to shooting guard from point guard when Nash is on the bench, and in Toronto he would give the Raptors some insurance behind Jose Calderon in case T.J. Ford is unable to return this season from his neck injury.
Stoudamire will be free to sign with any NBA team after he clears waivers at 6 p.m. ET Wednesday.
Chris Sheridan covers the NBA for ESPN Insider.