The 18-year-old has seemingly established himself as the Scottish Premiership leaders' first-choice in that position.
Despite only making two league appearances before this season, the 18-year-old has established himself as Ronny Deila's first-choice left-back this term, which appears to have played a part in the Honduran's decision to reportedly quit the club in the summer (via The Scottish Sun).
However, Tierney explained that the rivalry between the pair has not become difficult, and insisted that he wants the 29-year-old to stay at Parkhead beyond this season.
"He's definitely been one of the most encouraging of the players," he told The Scottish Sun.
"When I was just starting to train with the first team last season he took me under his wing, gave me a lot of tips and worked a lot with me on crossing. All that helped me progress.
"I hope he stays. He's a great player, a great guy and has been a good servant to the club. I'm sure that'll continue because he's a top professional.
"I can understand if he's not playing that he may look elsewhere."
Given how impressive the Scotland U19 international has been since being given a prolonged run in the side, it is hardly surprising that Izaguirre has felt that he needs to consider his options.
Tierney's age means that he will surely improve in the coming years, and while his performances remain at a high standard, Deila appears to be happy to allow his development to continue while playing first-team football.
And with Izaguirre's age meaning that he perhaps has one big move left before his ability begins to decline, it is understandable that if he cannot get back into the team, it may be the right time for him to move on.
And while Tierney admitted that he would understand if his rival did look to leave, it would surely be a big blow for his development if he was not able to turn to a player of Izaguirre's experience in the future.