The Gunners are keen to bring in the midfielder as a long-term replacement for Aaron Ramsey.
The Wales international is out of contract at the end of the season and is expected to end his 11-year spell at the Emirates after the club retracted their offer of a new deal.
Suarez is seen as Ramsey’s ideal successor and he is believed to have a £20m release clause in his contract, although Barcelona are reluctant to sell.
The 25-year-old has been starved of regular playing time at the Nou Camp in recent seasons.
And according to Spanish outlet Sport, Suarez has given a move to Arsenal his approval.
The report claims his agreement was essential before negotiations started and the two clubs will now discuss the terms of the transfer.
Suarez is out of contract next summer and Barca would prefer to cash in rather than risk losing him for free next year.