The 25-year old Honduran left-back has attracted plenty of interest after enjoying a stellar debut season with the Hoops which saw him take out numerous awards including the Scottish Premier League Player of the Year.
There has been speculation surrounding Izaguirre, with big clubs such as United and Liverpool circling, and although he admits that the Old Trafford giants did come in for him, he insists he is happy in his present environment.
"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."