Bayern have already snatched playmaker Mario Gotze from Dortmund and are hoping to tie up a deal for Lewandowski in the coming weeks.
However, the impressive Dortmund may well be resigned to losing their main man but they would prefer him to move to England rather than stay in the Bundesliga and strengthen their rivals squad.
Chelsea are set to hold fire on any transfer dealings until a new manager is in place but the chance to sign Lewandowski could be too hard for Roman Abramovich to turn down, especially if a deal for Atletico Madrid forward Radamel Falcao falls through.
Dortmund are hoping to bring Chelsea winger Kevin De Bruyne back to Germany after a successful loan spell at Werder Bremen this season and could be used as part of the Lewandowski deal.
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