The Sunday Mirror says that club owner Mike Ashley intervened in order to keep Given at the club. Ashley offered Given a six-year contract that would have seen him earn £50,000 a week.
But Given signed a four-and-a-half-year deal at Manchester City instead.
Kinnear told the Sunday Mirror: “My conscience is clear over the departure of Shay Given. I did everything in my power to keep him at Newcastle.
“I went to Mike Ashley and the board and asked them to make Shay a really good offer. The outcome was we were willing to pay him £50,000 a week, for six years. That would have taken him to 39.
“We were also willing to give him a role as a goalkeeping coach when he retired. I thought that would have sorted it out but City topped our offer.
“Long before I took the manager’s job I knew he was one of the best keepers in the world and there was no way that I wanted to lose him.
“I made my feelings known to the people that run the club but I don’t think his leaving was down to money.
“If it was then I think the contract he was offered would have been enough to keep him here. It was a very good deal.”