The left-back admits he would find it difficult to leave the Bhoys and is pleased with the bond he has with supporters of the Scottish champions.
As such, Izaguirre says he has no intention of leaving Celtic in the near future.
The 28-year-old told reporters: "My future is here at Celtic. I would find it very difficult to leave Celtic.
"Celtic have given me everything. I have six winners medals and I am about to win a seventh. The fans love me and I am grateful to them."
The claim doesn't help sort the 19-year-old's future out, of course, as Manchester City may well recall the defender ahead of next season.
But Denayer has nevertheless made a concrete admission that he would enjoy returning to Celtic. That should certainly favour the Bhoys when it comes to any potential negotiations with City...
“Of course I would be happy to do that,” said Denayer. “I’ve had a very good year at Celtic so far. I would be happy to come back."
Celtic travel to Dundee United on Sunday afternoon in their quest to secure a double, having missed out on the treble after being knocked out of the Scottish Cup last weekend.