According to SportsMole.co.uk, the Polish international recently denied reports that he had already agreed to join Bayern Munich, and admitted that he would like to play in England.
That news has alerted Arsenal and City, who want to boost their squads for the second half of the season, the report said.
Arsene Wenger could be prepared to spend up to 25 million pounds on Lewandowski, despite the fact that his Borussia Dortmund contract runs out in the summer, the report added.
The Gunners have made no secret of the fact that they want another striker and fear that they will miss out on previous targets Luis Suarez and Wayne Rooney, the report further said.
City meanwhile will sacrifice Edin Dzeko as part of the deal if required as the Bosnian has found himself on the sidelines under Manuel Pellegrini after an encouraging start, according to the report.
Dortmund have maintained that they will not sell their prized asset to rivals Bayern, so a big Premier League offer is sure to tempt them before he leaves as a free agent in the summer, the report mentioned. (ANI )