The veteran centre-forward's current Barca deal will expire at the end of the season.
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Lewandowski has been linked with Juventus and AC Milan in Italy, while options in MLS and the Saudi Pro League are also emerging.
Sport says Barca have now offered a new 12-month contract extension to the 37 year-old Poland international.
The deal involved an almost 50 per cent cut on his current salary, though also includes a catalog of performance and appearance bonuses to make up the difference.
Lewandowski is now considering the offer and will take his time before offering a response.