The Icelandic goalkeeper has reportedly undergone a medical ahead of a switch to the Emirates from Dijon, where he is expected to provide competition for No.1 Bernd Leno, with Emiliano Martinez seemingly set for a £20m move to Aston Villa.
However, some Gunners supporters were less than impressed when they discovered old tweets from Runarsson's account abusing their legendary former manager Wenger.
The Frenchman won three Premier League titles and seven FA Cups during his 22 year spell at the club, but split opinion towards the end of his reign after a number of less successful campaigns.
In July 2011 Runarsson tweeted: "Arsene Wenger is a little too stupid!" with the hashtag "French f***".
And a month later, by which time Arsenal had sold two of their best players in Cesc Fabregas and Samir Nasri, Runarsson added: "Arsene Wenger is definitely the dumbest man on this planet", while he also repeated the same hashtag.
The tweets have now been deleted.