Speaking at the launch of Salthill Devon's Galway Macron Cup in Drom, Kilbane was adamant that the improving Norwich City player should be ahead of Robbie Brady in the pecking order.
"I really cannot speak highly enough of Anthony because of where he has come from and what he has done to get to the top. He is very driven. I hope he is selected," he said. "Now is the right time to get him involved, and to make him feel welcome within the squad.
"For me, he is further ahead of Robbie because he has played more games and is playing consistently at Premier League level."
Kilbane feels that the return of Shay Given to the fold would also be beneficial. "I think Shay should come back – I don't think he should have retired in the first place. There is an argument to say youth should get its chance, but in my opinion Shay is still our best goalkeeper.
"Keiren (Westwood) and other goalkeepers would have an argument with that, but what Shay has done over the years is fantastic.
"I think the manager should pick him, and Shay has made it clear that he wants to be included. Hopefully they've had the conversation and Giovanni has listened to his point of view."
Kilbane also had a view on Eamon Dunphy's comments regarding Given's physical well-being. "I heard he said Shay looked overweight, but Shay has never been overweight in his career," Kilbane continued. "Shay is still our best goalkeeper. He didn't have a good Euros by his own standards, but how well has he performed for us over the years?
"Going into the Euros unfit, trying to get fit, he was taking pride in the jersey. That kind of stuff is sometimes forgotten when you don't perform to the levels that people expect."
According to Kilbane, addressing lingering communication difficulties is another problem Trapattoni must solve, particularly with Shane Long.
"I just hope that any sort of grievances that are there – there always seems to be something going on – are sorted," he added.
"Normally, things between a manager and a player – and it has happened to me at club level – can be buried very quickly. It needs only a phone call or a conversation. That has been Giovanni's problem over the years.
"When problems have started he has not been able to pick up the phone to ring the players just to nip it in the bud."