With both clubs in the market for firepower this summer, a trade agreement has been mooted.
Sanchez is considered to be a top target for City boss Pep Guardiola, with the pair having previously worked together at Barcelona.
Any move could see Aguero slip down the pecking order at the Etihad Stadium, despite being one of the Premier League’s most potent and reliable goalscorers.
Neither side has commented on the possible swap rumours and Arsenal legend Winterburn is not convinced a deal could ever be done, telling bwin: “It’s a minefield.
“But I can see where that link would come because they want a high-quality centre-forward and Aguero is certainly that. I don’t know with two high value players how easy it’ll be.
“I can’t remember when this sort of deal has actually happened in the past. Contract lengths are different and club’s valuations of players can change.
“I just wonder whether Arsenal have taken the view ‘if you keep pestering Sanchez, we’ll start talking about your players'.”
Winterburn added: “Would Sergio Aguero even want to come to Arsenal? Then you’re talking about involving agents with a swap deal and seeing how that all works.
“I think there’s a little bit of mind games going on.”
Aguero netted 33 times in all competitions for City last season, taking him onto 169 efforts in just 253 appearances for the club.
Sanchez, meanwhile, reached the 30-goal mark for the first time in his career as he proved to be a talismanic presence at Arsenal.
He has, however, seen his future called into question as he enters the final 12 months of his current contract.