The Celtic icon is impressed with the summer signing.
Indeed, the centre-back, who joined Celtic this summer after Virgil van Dijk left for Premier League side Southampton, had been speaking to reporters earlier on Thursday.
During his press conference, the 21-year-old spoke confidently about being the 'Celtic no.5 now' - and McAvennie has reacted positively to his attitude on Twitter.
He likes Simunovic's style. And the big centre-back will certainly need to show some of that confidence on the pitch in replacing Van Dijk.
Like you're style big man https://t.co/UGHPA8P4iT— Frank McAvennie (@MaccaFrank) September 10, 2015
Judging by first impressions, Celtic certainly have an imposing new player in Simunovic but, aged just 21, that confidence needs to be kept in check by Ronny Deila.
The Bhoys certainly won't want their defender to get over-confident so early in his Bhoys career. A comparable example was Lazar Markovic joining Liverpool and immediately declaring that he doesn't need time to settle in - and that he will hit the ground running at Anfield.
A couple of months later, after a terrible start, he was saying all he needs... is time. Several months later, he has now been loaned to Fenerbahce.
But that's just one example. McAvennie, for one, is impressed by Celtic's tough-talking Simunovic.