Trapattoni has named Given skipper in the absence of the injured Robbie Keane.
The Italian often compared Given favourably to his compatriot Gianluigi Buffon ... regarded by many as the best goalkeeper in the world.
Trapattoni: "I speak to two or three big managers who are friends and they ask me if they think Given can play in Italy with them.
"With his personality and quality, I feel he is as good as Gianluigi Buffon.
"I knew of Shay before because I have played against Newcastle, but now I have worked with him, I know his personality, how he trains and how he commands his defenders, and that's very, very important.
"I have spoken with two or three of the big managers who are my friends, and they have asked me if he could play in Italy.
"But the problem is in Italy, they spend the big money on striker and much less on goalkeepers.
"For me, the goalkeeper is as important as a striker. A goalkeeper normally makes two three vital saves in a season and a striker will score two or three very important goals, so both are very, very important."
Given: "From a man like Mr Trapattoni, it is a great honour for him to say such words because Gianluigi Buffon is known as one of the best goalkeepers in the world
"To be mentioned even in the same sentence as him is a great honour for me.
"It's all about opinions, I suppose."
Spurs are also interested in Given, and some sources in the London press this morning suggest if the bid was £6m, Mike Ashley would sell.