According to the 'Independent', representatives of the Barcelona man have entered into talks with a number of top Premier League clubs over a reduced £14m deal.
However, Arsenal are leading the chase as they search for a replacement for Aaron Ramsey, whose contract expires at the end of the season.
The Welshman is likely to leave the Emirates Stadium on a free transfer, after talks over a new contract broke down, and his role has been reduced under Unai Emery.
Furthermore, Suarez spent a season with Emery on loan at Sevilla, meaning that a working relationship has already been established.
It is hoped that this could give Arsenal the edge of Chelsea and Tottenham, with Suarez keen on a move after being privately told by Ernesto Valverde that he is surplus to requirements.