The Hall Of Fame was introduced to recognise some of the league's most successful individuals, with Alan Shearer Thierry Henry and Frank Lampard among those already inducted.
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With Sir Alex Ferguson and Arsene Wenger the first managers to be inducted, three more former players are set to make the cut.
Arsenal's title winning captain Tony Adams and a handful of Manchester United legends have all been included on the 15-man shortlist, including Rio Ferdinand, Michael Carrick, Andy Cole, Gary Neville and Nemanja Vidic.
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But while United have a strong standing in the nominations list, Goldbridge believes Irwin should have been included.
"The fact Denis Irwin isn't in there ahead of some of those is a joke," he wrote on Twitter.
"Recency bias and being in the media after retirement no doubt helps."
Irwin spent 12 years with United from 1990 to 2002, in which time he made 529 appearances for the club and scored 33 goals.
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In that time he won seven Premier League titles, two FA Cups, a League Cup, a Champions League, a European Cup Winners' Cup and an Intercontinental Cup.
The Republic Of Ireland legend wasn't only regarded highly by supporters though, with teammate Roy Keane describing him as 'a great'.
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He said of Irwin in 2021: "You are talking about the modern full-back; Denis could play at left-back, right-back, score a goal, good at set-pieces, very rarely injured, good personality.
"Denis was a great player. You are on about being consistent, Denis was an 8/10 most weeks."
And this was backed up by another former teammate in Gary Neville.
Responding to a football on Twitter on who didn't agree with him calling him the Premier League's best full-back, he added: "You didn't watch him play then?
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"Denis would play full back in any team of [Jurgen Klopp or Pep Guardiola's]! Left or Right! He didn't give goals away, didn't give the ball away, brilliant going forward and could take set pieces to the equal of most!"
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