The Poland international's current contract with the Bundesliga champions runs until June 2019, but he has been heavily linked with a move elsewhere in recent months.
Bayern are keen to hold on to the 27-year-old, though, and his agent recently confirmed they have opened talks over a contract renewal.
And Lewandowski himself has now made it clear he is ready to ink a new deal and disappoint PSG and Madrid.
"I know there is interest from abroad," the striker told Sport Bild. "But I can very well see myself signing a new contract with Bayern because of the great team we have.
"This club is known for its policy to reward good performances.
"Of course, I have seen how the club is preparing for the future. The contract renewals of Jerome Boateng and Thomas Muller was a sign that Bayern can hold on to its star players regardless of the money in England."
Lewandowski has been in stunning form this campaign, scoring 21 goals in 20 Bundesliga appearances.