Wade says Oswalt's agent, Bob Garber, contacted Houston owner Drayton McLane earlier this week to make the request.
Wade says he wants to win with Oswalt on the Astros. Houston went into Friday night's game against Tampa Bay with the worst record in the National League at 14-27.
Oswalt has made nine straight quality starts to open the season but is 2-6 despite a 2.66 ERA. He has gotten the lowest run support in the league.
The 32-year-old Oswalt has a no-trade clause in his contract. He recently said he would be willing to waive it.