The Borussia Dortmund hitman will join Bundesliga rivals Bayern in the summer when his Dortmund contract runs out but his Polish team-mate Szczesny tried to get to join the Gunners instead.
"We had several talks about this. It was him who did most of the talking, how the club looks inside, what Arsene Wenger thinks of me.
"When we trained before the Champions League games at Colney, there were important people from Arsenal at our sessions as well."
Lewandowski has scored 16 goals for club and country this season including the winner at the Emirates when Dortmund beat Arsenal 2-1 in the Champions League.