Scholes won the 10th Premier League title of his illustrious career on Saturday after coming on as a second-half substitute to help United secure the point they needed to guarantee first place in a 1-1 draw at Blackburn.
But the 36-year-old is believed to be considering his future as he is no longer a regular in Sir Alex Ferguson's starting line-up and has started only 22 games in all competitions this season.
Ferguson wants Scholes to sign another one-year contract for next season like his equally experienced colleague Ryan Giggs.
But the former England international has so far given no indication about his plans and Gill is aware there is a reasonable chance he will decide to hang up his boots.
Speaking to BBC Radio 5 Live's Sportsweek programme, Gill conceded Scholes could opt to follow United team-mate Gary Neville into retirement.
"It wouldn't surprise us if Paul Scholes retired," he said.
"On the hand, we are enjoying the success we are having, so at the end of the season, he will have a conversation with Sir Alex about that.
"I am sure he will let us know his decision and we will respect it. He has been a brilliant player for many years.
"It is interesting that while Ryan got his 12th title yesterday, that was Paul's 10th.
"It shows what he has achieved for us and what an absolutely fantastic player he has been."
Ferguson already has to look for a replacement for Dutch goalkeeper Edwin van der Sar, who has announced he will quit football after United's Champions League final against Barcelona on 28 May.
Tomasz Kuszczak's nervous performance at Blackburn on Saturday underlined United's need for a quality replacement when the 40-year-old Van der Sar retires.
Atletico Madrid's David de Gea has been linked as their main target but Gill would only confirm they have identified the man they want to sign.
"We know the keeper we want," Gill said. "We are in a good situation with that and it will progress at the end of the season.
"It is not as though it is a surprise that Edwin is retiring. We have been associated with all the top goalkeepers in Europe for the last six to 12 months.
"We have made the decision and I am sure we can get the deal done."