Pressly said at his introductory press conference with the Cubs on Wednesday that he was told by the team he would close some games this season, Meghan Montemurro of the Chicago Tribune reports.
Jeff Passan of ESPN.com reported Sunday that Pressly is waiving his no-trade clause and will be traded from the Astros to the Cubs.
Pressly pitched 1.2 scoreless innings while allowing two hits to earn the save Saturday against the Angels.
Pressly (2-3) allowed one earned run on one hit and one walk while striking out two to earn the win Thursday against the A's.
The Astros activated Pressly (back) from the 15-day injured list Thursday, Ari Alexander of KPRC 2 Houston reports.
Pressly (back) threw a live batting practice session Monday, Brian McTaggart of MLB.com reports.
Pressly (back) threw another bullpen session Saturday and is expected to return from the injured list when first eligible, MLB.com reports.
Pressly (back) threw a bullpen session at Minute Maid Park on Wednesday, Chandler Rome of The Athletic reports.
Astros manager Joe Espada said that Pressly (back) played catch Monday, MLB.com reports.
The Astros placed Pressly on the 15-day injured list Saturday due to a lower back strain, Matt Kawahara of the Houston Chronicle reports.