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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.