Robson, a former Arsenal midfielder who until last year worked for the club's in-house TV station, launched a scathing attack on Wenger prior to the Gunners' 3-1 defeat to Bayern Munich on Thursday evening.
"I hope it [Wenger's exit] is sooner rather than later because I certainly won't miss him because Arsenal have been going down the wrong road for quite some while," Robson told the BBC.
|PRESSURE ON WENGER
|9/1||Arsenal are 9/1 with Coral to beat Aston Villa 3-1
Robson also blamed Arsenal's eight-year trophy drought on the 63-year-old and claims the Frenchman "doesn't do much coaching" and "doesn't have an actual game plan".
Wilson, however, believes Robson is hitting out at Wenger because he is no longer employed by Arsenal.
"This is a guy who worked for this club up to a few weeks ago, doing the pre-match stuff on the opposition, who then went to a newspaper, without naming anybody who had given him the so-called facts about him [Arsene Wenger] being a dictator," Wilson told the BBC.
"Today, he's been on every half hour on Radio Five Live, and this is a guy who obviously is a bitter guy because he's no longer got a role or any employment here."