The 21-year-old initially joined Los Blancos in 2011, spending nine years in their academy system before representing Real Madrid B between 2020 and 2022.
Gutierrez also made 10 appearances for Real Madrid's first team during his time at the club, featuring on six occasions during the 2020-21 campaign and four times in 2021-22.
The Spain Under-21s international made the move to Girona last summer, though, with Los Blancos allowing him to leave despite Marcelo's departure.
There has recently been speculation surrounding Gutierrez, with Carlo Ancelotti's side having issues at left-back this season due to Ferland Mendy's injury problems.
Gutierrez has been in strong form for Girona during the 2022-23 campaign, featuring on 21 occasions in all competitions, contributing three assists in the process.
The Spaniard has said that Madrid has 'always been his home', and he is eyeing a return to the reigning Spanish and European champions.
"Of course, these are things that I have in my head, Madrid has always been my home, and thanks to the club, I am the player I am now. It's clear to me that I have to keep doing well at Girona and in the summer we'll see," AS quotes Gutierrez as saying.
"In football, you never know what's going to happen. Returning to Madrid, to my home, would be very nice, but it's all about having a great season here, as I'm already doing, and having good numbers."
Eduardo Camavinga is currently being used as a left-back due to Mendy's absence, with Real Madrid also having problems on the opposite side due to recent issues for Dani Carvajal and Lucas Vazquez.
Carvajal has now returned to fitness, though, with the defender in the squad for Wednesday's Club World Cup semi-final against Al Ahly.
Al-Hilal recorded a 3-2 victory over Flamengo in Tuesday's first semi-final, meaning that the winner of the second last-four clash will take on the Saudi Arabian side in Saturday's final.
Real Madrid will enter the contest with Al Ahly off the back of a 1-0 loss to Mallorca in La Liga on Sunday afternoon.