The 28-year old left-back has been with the Scottish champions since 2010, picking up three Scottish Premierships and two Scottish Cups along the way.
Izaguirre is currently in Florida with the Honduras national team preparing for the 2014 World Cup in Brazil but took some away from his duties to speak of his desire to stay at Celtic Park and achieve further success before turning his hand to management.
"If Celtic decided to sell me, then no problem, but my desire is to stay with them, play and win titles and play in the Champions League," he said.
"That's what you will remember for the rest of your life. I want to be part of Celtic for many years to come.
"My dream is to one day return to Honduras and prepare to become a great manager. Motagua is my team, but I am a professional and would coach anywhere."
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