Lewandowski, who has a year left on his deal at the Allianz Arena, has publicly stated that he wants to leave the Bundesliga champions this summer.
The 33 year old striker scored 35 goals in just 34 Bundesliga games as Bayern Munich won the Bundesliga last season.
He scored a total of 57 goals in 55 games for club and country last season.
Barcelona, Chelsea and Manchester United are all reportedly in the race to sign Lewandowski this summer.
However, Sutton has warned the Poland goal-machine to snub a move to Manchester United and join rivals Arsenal instead.
According to Sutton, he can’t see why Lewandowski would want to go to United and thinks Manchester City, Liverpool, Chelsea, Tottenham and Arsenal would all be more preferable choices.
Sutton told BBC Radio 5 Live: “I have seen that Lewandowski has been linked.
“If he doesn’t go to Barcelona, then he will go to Manchester United.
“But why?! Why would he want to go to Manchester United? There are bigger and better options out there.
“Manchester City, Liverpool, Chelsea and Spurs, at this moment in time and Arsenal are a better option, at this moment in time than Manchester United.
“One club seems to be stable under Arteta, I am not saying Arteta has torn up too many trees, but they are in a better position and they are better placed than Manchester United.”
Since joining Bayern Munich from Borussia Dortmund, Lewandowski have scored 344 goals and provided 77 assists in 374 appearances, which is a truly sensational record.
Lewandowski reportedly earns £329,000-a-week at Bayern Munich and wants £400,000-a-week from clubs interested in signing him.
Manchester United are currently undergoing a period of transition, with new manager Erik ten Hag taking over from the disappointing interim period of Ralf Rangnick.