Izaguirre revealed on Saturday that Manchester United were keen on signing him.
“It was a fabulous season and it went so well that it seems like a dream,” he said in the Daily Record.
“I have no words to describe how happy I am in Glasgow, especially now my family live with me.
“It is true that there were offers from Manchester United and other clubs.
“But I don’t think anything will happen. My hope is to stay at Celtic.
“My aim is to recover to full fitness quickly so I can play again with my club.”