The 27-year-old midfielder has been out of action since February with an abductor problem.
"I'm still a wee bit from training with the first team but, if everything goes well, hopefully I'll be back for the Cup final," Sky Sports News quotes Brown as saying.
"That's my target but it will be touch and go. It's going to be hard to get some game time in before it as well."
Celtic take on Hibernian in the Scottish Cup final at Hampden Park on May 26.