The 31-year-old has been at Stamford Bridge since 2007 when he was signed by former manager Jose Mourinho.
The paper reports that the wide midfielder is seen as expendable under new coach Andre Villas-Boas, and Arsenal are looking to swoop.
Since Arsenal manager Arsene Wenger saw his side demolished 8-2 on Sunday against reigning Premier League champions Manchester United his club’s transfer activity has increased significantly.
The Gunners have already wrapped up a move for Brazilian left-back Andre Santos from Turkish side Fenerbahce for £6.2m (€7m).
The Sun are also reporting that centre-backs Gary Cahill and Alex are being chased by Wenger, however, the potential signing of Per Mertesacker throws interest in the duo up in the air.
Mertesacker, 26, is captain at Bundesliga club Werder Bremen and is expected to undergo a medical in London on Tuesday.