Scholes, 36, helped United clinch their 19th Premier League title on Saturday, coming on as a substitute in the 1-1 draw at Blackburn Rovers that took them over the line.
The champions already know they will need a new goalkeeper, with Edwin van der Sar to retire at the end of the current campaign, and the new season may mark the start of the post-Scholes era too.
"We don't know what Paul Scholes is going to do," Gill said in an interview with BBC Radio 5 Live. "He may decide he'd like to retire at the end of this season, though we're very much prepared and happy to offer him a further year."
"Edwin has had a fantastic career and has been absolutely brilliant this year," Gill said.
"We know the keeper we want and we're in a good situation with that. That will progress at the end of the season. We've made the decision and I'm sure we can get the deal done.
"Obviously there's been a lot of speculation and we've been associated with all the top goalkeepers over the past six to 12 months. But we've known who we've wanted for many months and we aim to achieve that."
United will cap their 12th Premier League title win under Sir Alex Ferguson with the club's fourth European Cup triumph if they beat Barcelona in the Champions League final at Wembley on May 28.
"Without doubt there's going to be some activity in key areas of the club," Gill said. "But it's not as if we're starting work on that now. We've been preparing for that for the last 12 months.
"We'll get on with it and see in the summer what we achieve, which will hopefully ensure that Alex has the players he needs to push on and have another successful season."
