There has been speculation linking the Scot with a move back north of the border after just a year in Hull, and Taylor says that if there was interest then the 30-year-old could be on his way.
The City boss said: "I would not really want to lose him. He's a very good pro and a very good player to work with. He did tremendously well last season but if any clubs do come in we would have to think about it."
But Taylor says that no offers have been received so far: "I sometimes wonder where these reports come from. No-one has approached me or the chairman and you would think we'd have heard something.
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"John isn't upset by the speculation. He's seen and heard it all before. He takes it all in his stride. He's training very hard and is looking forward to the new season."
Meanwhile, chairman Adam Pearson says that City are looking to cut down the wage bill.
He said: "Peter and I have sat down and discussed the situation and we both agree that the squad is too big for next season.
Meanwhile, chairman Adam Pearson says that City are looking to cut down the wage bill.
He said: "Peter and I have sat down and discussed the situation and we both agree that the squad is too big for next season.
"Ideally, we'd both like to see 24 or 25 players and I think Peter would be happier working with that figure. We'd still have cover for all positions and, at the same time, we'd be able to bring some of the younger players through in the reserves.
"At the moment, the market is pretty sluggish but hopefully things will start to pick up over the next couple of weeks as clubs build-up to the new season."