The 20-year-old made his breakthrough with the Amsterdam giants under Erik ten Hag and has continued to play a key role since Jonny Heitinga took charge.
Primarily operating as a right-back, Rensch has scored three goals and set up one more in 23 Eredivisie appearances this season, as well as starting three Champions League group-stage games.
Since progressing through the club's academy ranks, the Netherlands international has produced seven goals and five assists from 89 outings in an Ajax shirt, winning two Eredivisie titles and a KNVB Beker in the process.
Rensch, who was a part of the Netherlands' Under-17 squad during their European Championship triumph in 2019, made his debut for the senior Oranje team in a 6-1 thrashing of Turkey in September 2021, although he has not returned to the first-team setup since.
Rensch is only contracted to Ajax for another two years, and the Eredivisie giants' resolve could supposedly be tested this summer by both Man United and Liverpool.
Now, Football Insider claims that Arsenal are also keeping tabs on the 2003-born youngster, who is also capable of playing in the heart of defence or as a left-back.
The report adds that the Gunners have earmarked Rensch as an ideal alternative if they do not land Real Valladolid's Ivan Fresneda, who is understood to be their number one right-back target.
While Arsenal are not giving up hope of luring Fresneda to the Premier League, they could lose out to Borussia Dortmund, who are thought to be making progress in talks over a £20m deal for the Spanish teenager.
As a result, the North London club could turn their attention to Rensch, whose potential has supposedly left Gunners chiefs "very excited" as Mikel Arteta tries to bolster his options on the right.
The Arsenal boss has deployed Ben White in that full-back role for the majority of the campaign, relegating the injury-plagued Takehiro Tomiyasu - who is out for the season due to a knee problem - down to second choice.
However, Arteta is understood to be planning to revert White to a central position for the 2023-24 season and is therefore seeking further cover on the right-hand side of the field.
Brighton & Hove Albion are also rumoured to be attentive to developments surrounding Rensch, who recently missed five Eredivisie games with a thigh injury before returning for Saturday's goalless draw with AZ Alkmaar.
Arsenal cut the gap to Premier League leaders Manchester City down to one point thanks to Sunday's 2-0 win at Newcastle United and return to the Emirates to face Brighton & Hove Albion this weekend.