It is understood that the Poland captain is determined to quit his club and his next destination would be revealed in few weeks time.
Despite being under contract until 2021, he has hired super-agent Pini Zahavi to see off his contract to release him from the Bundesliga leaders.
But Zahavi faces an uphill challenge, with Bayern not short of funds and expected to resist any attempts to lure their prized goal scorer away.
The Premier League teams are likely to face stiff competition from Real Madrid – and PSG will also join the hunt if, as expected, Edinson Cavani leaves in the summer.
Since signing in July 2014, Lewandowski has scored 97 goals in 108 Bundesliga games for Bayern – and six in his last four games.
Meanwhile, Lewandowski laughed off suggestions that his split from Zahavi means a move away from the Bundesliga champions is inevitable.
Lewandowski, 29, parted with Cezary Kucharski, his agent of 10 years, sources close to the player confirmed to ESPN FC last week, while earlier this month, Marca reported that Kucharski had “offered” Lewandowski to Real Madrid.