The 22-year-old began his career with Real Madrid and made just 10 senior appearances after breaking through from their academy, before joining Girona in the summer of 2022.
Gutierrez has since established himself as a first-team regular with Girona and has been a key part of the side that have surprisingly challenged Real Madrid for the La Liga title this season.
After making 34 La Liga appearances in his first season with the White and Reds in 2022-23, Gutierrez has since started 26 top-flight matches this term for Michel's side, scoring once and registering four assists.
Real Madrid allegedly retain 50% of Gutierrez's rights as well as a sell-on clause, while a recent report claims that they also have the option to re-sign the defender for just €8m (£6.8m) this summer.
Both Los Blancos and Man United have been credited with an interest in Gutierrez, who is under contract at Girona until June 2027.
However, Fichajes reports that Arsenal are the latest club to enter the race for the signature of the highly-rated left-back.
The report claims that Man United have identified Gutierrez as their 'top target' and are determined to lure him to Old Trafford this summer, with Erik ten Hag keen to bolster his left-back options amid injury concerns with both Luke Shaw and Tyrell Malacia.
Arsenal, however, are said to have also shown significant interest in the youngster, with Mikel Arteta another manager who would like to strengthen his options on the left side of defence.
Arteta has predominantly used Oleksandr Zinchenko at left-back this season, with the Ukraine international starting 17 games in that position across all competitions.
Jakub Kiwior and Takehiro Tomiyasu have also operated on the left side of a back four for the Gunners this term in the absence of Zinchenko, while versatile defender Jurrien Timber - who has been sidelined for the majority of this season with an ACL injury - is regarded as another left-sided option at Arteta's disposal.
Arsenal could have an advantage over Man United in the race for Gutierrez, as they have a stronger chance of qualifying for next season's Champions League, which could prove to be a determining factor for the left-back when deciding his next career move.
The Gunners are thought to be prioritising the addition of a new centre-forward this summer, though, with Napoli's Victor Osimhen and Brentford's Ivan Toney believed to be high on their list of targets.