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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.