Both clubs face strong competition from Bundesliga giants Bayern Munich in the race to sign the striker.
The 25-year-old Pole has insistd that his move to Bayern Munich is not a done deal, despite reports suggesting he is set to joing the club.
Lewandowski’s current contract with Borussia Dortmund is set to expire at the end of the season.
The Sunday Mirror reports that Arsenal are reportedly prepared to pay £25million to land Lewandowski in the January window before he becomes a free agent next summer.
“I don’t think it is a real big surprise that I have expressed a desire to play in England at some point in my career,” said Lewandowski.
“The Premier League is one of the best and most exciting in the world because it is attractive for most of the world’s top players.”
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?