The Englishman has started the season in ominous form after a summer of transfer speculation, and the Red Devils' former chief executive believes a new contract may follow
Rooney spent the summer trying to engineer a move away from Old Trafford with Chelsea his most determined suitors, but United were determined not to sell their star man to a rival.
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When asked on BBC Radio 5live whether he thought Rooney could be offered a new contract, Gill replied: "Without doubt, I'm sure they would look at it.
"We had an approach to dealing with players' contracts at Manchester United that's stood us in good stead for many years and I'm sure that Ed [Woodward, executive vice-chairman] and David [Moyes] and the owners will continue with that policy."
Gill also refused to comment on suggestions that United have privately admitted Rooney never asked to leave Old Trafford, despite Sir Alex Ferguson's assertion to the contrary back in May.
"I'm not going to comment on that situation," he added. "I know you'd like me to say what I know. But I'm not going to. I think it's important to move forward now."