The Gunners were frustrated in their attempts to land the controversial Uruguay international before Monday's deadline, failing with a bid just £1 over £40m which they wrongly thought would trigger a release clause in his contract.
Suarez made it clear in June and July that he wanted to leave Anfield for a club playing in the Champions League but the Reds stood firm and insisted he wasn't for sale at any price as he was under a long-term contract.
The forward was unhappy at first and attempted to force through a move but in the end accepted the club's stance and is finally set to return to action later this month when his 10-game ban for biting Chelsea's Branislav Ivanovic at the end of last season comes to an end.
However, Arsenal remain keen on the former Ajax man and will monitor his progress when he is back in Brendan Rodgers' side with a view to making a huge New Year offer for the 26-year-old.
Liverpool are believed to have privately told Suarez that he can move on next summer to a Champions League club if they fail to make the top four this term but will look at the situation again in January - giving the Gunners hope they could still land him.