The Sun reports that the two Premier League giants are keen on signing the 26-year-old midfielder.
Krychowiak has become a key player at Sevilla and Arsenal boss Arsene Wenger wanted to sign the midfielder in the January transfer window.
Wenger will make a new move for Krychowiak this summer as both Mikel Arteta and Mathieu Flamini looks set to leave the Gunners at the end of the season.
Arsenal face competition from the likes of Manchester City, Real Madrid and Juventus.
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Being an amiable guy is good for you and Jurgen Klopp is living proof.
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.