The likes of Manchester United, Manchester City and Chelsea have also been linked with the 27-year-old who is widely regarded as one of the world’s best number nines; however, the Bernabeu was understood to be his preferred destination.
But with Karim Benzema performing so well for Los Blancos, there’s every chance Real Madrid will decide not to swoop for Lewandowski this summer - and the Pole is now prepared to commit his future to the Bundesliga giants.
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This is according to Goal, who understand Lewandowski is ready to snub a big-money move to the Premier League in favour of putting pen to paper on a new contract at the Allianz Arena.
"I know there is interest from abroad," the world-class striker told Sport Bild, per Goal. "But I can very well see myself signing a new contract with Bayern because of the great team we have.
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"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."
Perfect time for Lewandowski to sign new deal
Lewandowski’s current deal doesn’t expire until June 2019 but the player - and no doubt his agent, too - clearly believe this is the ideal time to negotiate a huge contract.
The former Borussia Dortmund striker’s stock is higher than it’s ever been before - he’s scored 21 goals in 20 league appearances this season - but there are no guarantees his purple patch will last for the next three years.
Lewandowski will be close to 31 by the time his current contract expires and, unless he successfully negotiates a new deal over the next few months, his next one could be for significantly less money due to his advancing years.
Pep Guardiola might try to bring him to City
Pep Guardiola recently named Lewandowski as the most professional player he has ever met - high praise when you consider he’s worked with the likes of Xavi, Lionel Messi and Carles Puyol - and Manchester City would offer the player more money than Bayern Munich if he wished to follow his current manager to the Etihad Stadium this summer.
But it seems that unless Real Madrid are the club knocking, Lewandowski would prefer to stay put at Bayern Munich - a decision that looks very sensible with Carlo Ancelotti due to take the reigns at the end of the campaign.
Should Robert Lewandowski sign a new contract with Bayern Munich? Have your say by leaving a comment below.