The Uruguayan striker has been at the centre of transfer speculation all summer and has faced an uncertain future on Merseyside ever since biting Chelsea's Branislav Ivanovic and receiving a 10-match ban toward the end of last season.
Real Madrid were understood to have led the race for his signature should he opt to leave Liverpool, and this bid by Arsenal is a signal of ambition and a change of transfer policy at the Emirates.
The offer was turned down instantly as the Reds battle to keep hold of the 26-year-old, who was the club's leading goalscorer last season and the second highest in the division behind only Manchester United's Robin van Persie.
But the ex-Ajax man has shown frequent signs that he is unhappy at Liverpool and has in the past made no secret of his ambitions to play in the Champions League.
That is something both Real Madrid and Arsenal could offer next season and while the Spanish giants are still favorites, given that the player has previously complained about England and the way he has been treated by the media in this country, the bid by the Gunners remains an ambitious one and a clear sign that things are changing at the North London club.
Wenger has £70 million to spend this summer and the bid for Suarez is just another example of his ambitions for next season as the French manager seeks to end an eight-year wait without a trophy.