Scholes helped secure his 10th Premier League title when he was introduced as a second-half substitute in United's 1-1 draw at Ewood Park.
Manager Sir Alex Ferguson is eager for Scholes to sign a one-year contract extension, like long-time team-mate Ryan Giggs. However, the 36-year-old has his reservations after starting just 22 games in all competitions this term and has so far given no indication about his future plans.
Pefect 10: Paul Scholes (right) celebrates yet another title triumph
United have no intention of rushing the midfielder into a decision and Gill, like his manager, would prefer Scholes to continue. However, speaking to BBC Radio 5 Live's Sportsweek programme, Gill has admitted Scholes could opt to follow fellow old-stager Gary Neville into retirement.
'It wouldn't surprise us if Paul Scholes retired,' said Gill. '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.'
The uncertainty over Scholes' future merely adds to the confusion over United's summer plans.
Long-serving defender Wes Brown seems certain to leave, as does Michael Owen, whose two-year deal expires this summer.
On the move? Michael Owen's deal expires this summer and the striker looks set to leave Old Trafford
Owen Hargreaves is another who appeared destined for the Old Trafford exit door, although it is thought he is considering a one-year pay-as-you-play deal to remain with United.
Danny Welbeck and Tom Cleverley are both expected to return from impressive loan spells at Sunderland and Wigan respectively, while star names in the form of Wesley Sneijder and Ashley Young continue to be linked with an Old Trafford move.
It does seem Ferguson knows who he wants to replace Edwin van der Sar, though. Tomasz Kuszczak's hesitant performance at Blackburn merely emphasised how important it is that Ferguson gets his choice correct when the 40-year-old retires this summer.
And, although Gill did not name Atletico Madrid's David de Gea, after all the intense speculation surrounding the 20-year-old, it does appear he was the man being referred to in the chief executive's upbeat assessment of the situation.
Prime target: Atletico Madrid goalkeeper David de Gea is on United's shopping list
'We know the keeper we want,' said Gill. '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.'
Of course, the major upheaval will come when Ferguson decides to end his own career, although the United boss has already confirmed that will not be this summer.
Jose Mourinho has long been touted as a potential successor but the undignified manner with which he dealt with recent clashes against Barcelona has raised major question marks over whether he is the right man for the job.
Gill, understandably, was reluctant to get drawn into that debate. However, he did admit Mourinho's conduct would be discussed should United ever ponder making an appointment.
'I am not going to speculate about what is going to happen,' said Gill. 'That is in the future and it is wrong to speak about other clubs and their situation. We will discuss that internally and whatever impact that would have if he was in the frame many years down the line.'
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Explore more:People: Alex Ferguson, Paul Scholes, Tomasz Kuszczak, Michael Owen, Ryan Giggs, Ashley Young, Danny Welbeck, Wesley Sneijder, Wes Brown, Gary Neville, Edwin Van Der Sar, Jose Mourinho, David Gill, Owen Hargreaves Places: Barcelona, Europe