"We think it's personally insulting to probably the best goalkeeper in the Premier League.
"I don't want to lose him - I'm fighting a relegation battle, I want to keep every player and add to it, not lose it, but I really don't know."
On Tuesday, Newcastle keeper Steve Harper, who is a long-term second choice behind Given, signed a new three-year deal with the club.
Given joined Newcastle in 1997 from Blackburn for £1.5m and had made 461 appearances for the Magpies.
Meanwhile, Kinnear says he is still hopeful of signing Toulouse right-back Albin Ebondo.
"We're still tied up in negotiations," said Kinnear.
"The original price was £2.5m but (Toulouse) moved the goalposts and it's now £3m. We are still out in France negotiating. It's been two weeks now, so we have to wait and see."
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