But now they are set to move again - and Suarez has hinted he WOULD join the Gunners.
The 26-year-old Uruguayan ace wants Champions League football and to be at a club that are challenging for the title.
Arsene Wenger has been given £70m to spend to get the Gunners doing just that.
Suarez said: "If I receive an important offer to progress my career, I will study it.
"Some clubs have asked about me but I hand questions over to my agent. I am no stranger to rumours.
"I always want to improve. That's why I left Ajax for Liverpool.
"But this club needs to fight to enter the Champions League and, when it doesn't happen, it damages the morale of any player. So I've suffered.“It is hard to view the Premier League every week with never a chance of winning it”Luis Suarez
"It is hard to view the Premier League every week with never a chance of winning it."
Real Madrid remain the favourites to sign Suarez, who has again reiterated his displeasure at the English press.
Suarez has found himself in hot water after being banned for racial abuse of Patrice Evra and for biting Branislav Ivanovic.
"After the Evra incident, it was very difficult to convince people about the 'real' Luis Suarez. Things had improved but then the incident involving Ivanovic was another blow.
Arsenal are also interested in Gonzalo Higuain, Wayne Rooney and Cesc Fabregas.