Brown, 56, has two years remaining on his contract, but also has been contacted by the Boston Celtics.
The Pacers finished this season 39-43, the third losing season in Brown's career.
Brown has been at his home in Los Angeles, where his wife, Shelly, was expected to give birth today to the couple's second child, a daughter.
Croce, who has been vacationing, was unavailable for comment. Since expressing his interest in Kentucky coach Rick Pitino, Croce has said he would not discuss specifics of his search.
``[Brown's] a great coach, but I won't try and keep him if he wants to leave,'' Walsh said. ``He told me he wants to sit and think, but he knows I need a decision quickly.''
Brown was contacted by Celtics owner Paul Gaston and special assistant Larry Bird.
A third party, working on behalf of Croce, contacted Walsh earlier this week.
``I'm not comparing Indiana to anybody, I'm not trying to bargain,'' Brown told the Indianapolis Star-News.
``My focus is, should I come back or not?I want to do what's right by everybody.''