Given is interesting Hoops boss Neil Lennon.
Gennoe told the Scottish Sun: "I've felt a great degree of sympathy for Shay over the last 12 months in that for some reason Roberto Mancini has looked beyond him for Man City's No 1.
"He has exceptional potential and has become England's first choice. But Shay is still such a good goalkeeper that I'd never go against him. He deserves to be playing more regularly.
"Despite his lack of regular action he's still been producing top-class performances for the Republic of Ireland and that says it all about Shay and the standard he strives to maintain.
"Going back to Celtic would effectively be his career going full circle - and I'd be thrilled to see him back there. It's a club that means a great deal to both of us. I loved my time there and even after Shay left Celtic for Blackburn, then Newcastle United, he still talked about the club often as a big supporter.
"Celtic is a club that places a massive pressure on goalkeepers, but Shay could handle that no problem."