Republic of Ireland coach Trapattoni admitted earlier this week that he had spoken to coaches in Italy about the Magpies stopper.
Trapattoni believes Given has the ability to be rated on a par with Italy's number one Gianluigi Buffon and his comments led to suggestions he was touting the shot-stopper to Serie A clubs.
Newcastle's interim manager Kinnear is unhappy with the Italian's views on Given and hopes Trapattoni was merely trying to curry favour with the 32-year-old.
"I think it's a little bit disrespectful," said Kinnear on Sky Sports News.
"Shay, I think, has got another three years here on his contract.
"Why on earth Giovanni would want to bring out a statement like that I don't know - maybe he was just getting on the good side of Shay."
Given has spent over a decade at St James' Park and has recently been linked with a move to Newcastle's Premier League rivals Tottenham.
World Soccer Shop is offering some great SALE prices on first rate official team soccer jerseys. Check them out.