Arsenal, Fulham and Celtic have all been linked with the shot-stopper, who played 44 times for the Blues last season while Joe Hart was on loan at Birmingham City.
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However, Given has been relegated to the substitutes' bench so far this season while Hart has excelled between the sticks against both Tottenham Hotspur and Liverpool.
The 34-year-old is believed to be wanted by Arsene Wenger, Mark Hughes and Neil Lennon having fallen down Roberto Mancini’s pecking order.
But a move to either Emirates Stadium or Craven Cottage is thought to hinge on the future of Mark Schwarzer.
The Australian has been linked with a move to the Gunners throughout the summer as Wenger seeks a more experienced stopper to replace the inconsistent Manuel Almunia and Lukasz Fabianksi.
Nevertheless Ireland, who made his Villa debut in the 6-0 drubbing by Newcastle United on Sunday, believes Given must move on to gain regular first team football.
“I would like to see Shay go. He needs to be playing every week," he said.
"He is far to good to be left sitting on the bench. He is a brilliant person and the best goalkeeper I have ever played with.
“He deserves first team football.”
By Tom Eastwood
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