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The Poland international only arrived at the Parc des Princes last summer.
But The Sun claim PSG are prepared to let him leave after he struggled to make his mark in France.
The newspaper credit Arsene Wenger, as well as Manchester City manager Pep Guardiola, as long-term admirers of the defensive midfielder.
And they suggest the Arsenal gaffer is on the lookout for cover for injured Emirates ace Francis Coquelin.
Krychowiak cost PSG almost £28.6m when they signed him from Sevilla.
Although The Sun suggest Unai Emery may allow him to go out on loan as he freshens up his squad.
Krychowiak was a key part of the Sevilla side which won back-to-back Europa League titles in 2015 and 2016.
He has made just 10 Ligue appearances this term though.
PSG currently sit third in the French top flight, five points adrift of Nice.