The Honduran international defender has had to accept playing back-up to Kieran Tierney in the past two seasons.
However, the 31-year-old, who will fly out of Glasgow with the rest of the Celtic squad today for pre-season training in Austria, has indicated he is keen to commit his future to the Parkhead club.
Izaguirre still made 18 appearances for Brendan Rodgers’s side in the last campaign as they went undefeated domestically and won the Premiership title, the Scottish Cup and the League Cup.
“It would be great for everyone if he was to sign a new deal with the club.
“In terms of both a player and a person, I don’t think Celtic could ask for anyone better.
“I am sure the manager will be delighted with Kieran. He is playing very well, is an Invincible and a treble-winner. He has got the whole lot.
“But Emilio is a great player in his own right. You don’t have six league winners’ medals without knowing what you are doing.
“I played in his position and know what is required. Emilio is a proper Celtic full-back.