The 22-year-old has been in eye-catching form for La Liga title challengers Girona this season, making 27 appearances in all competitions, scoring once and registering five assists in the process.
Both Arsenal and Manchester United have been credited with an interest in the left-back, with the Premier League duo believed to have scouted him on a number of occasions this season.
Gutierrez made the move to Real Madrid from Getafe in 2011, spending nine years in their academy system before debuting for the first team in 2021.
The Spaniard made 10 appearances for the senior side before moving to Girona in August 2022, and he has now played 63 times for the Catalan outfit, scoring three goals and registering nine assists in the process.
According to Marca, Real Madrid have the option to re-sign Gutierrez for just €8m (£6.8m) during the upcoming summer transfer window.
Ancelotti is said to be an admirer of the full-back, and the Italian was asked for his thoughts on a possible return during his press conference on Friday afternoon.
The Real Madrid head coach said that the club will ultimately make the final call in terms of potentially re-signing him, and he is confident that "the right decision" will be made.
"All the players in Miguel Gutierrez's situation are controlled by the club. Miguel has done well at this stage and in the summer we will make the right decision again," Ancelotti told reporters.
Ferland Mendy and Fran Garcia are currently the two senior left-backs at Real Madrid, but there has been speculation surrounding the futures of both players.
Bayern Munich's Alphonso Davies is thought to be the capital club's leading target in that area of the field, with La Liga president Javier Tebas recently talking-up a possible move for the Canada international.
However, if both Mendy and Garcia leave, Gutierrez could potentially be re-signed as back-up to Davies due to the small fee involved.
Gutierrez is set to feature at Bernabeu on Saturday evening, with Girona heading to Real Madrid for a top-of-the-table clash in Spain's leading division.
The defender's contract with Michel's side is due to run until June 2027, but there is said to be a release clause of €35m (£29.9m) for clubs other than Real Madrid.