The 22-year-old has been in excellent form for his Dutch club during the 2023-24 campaign, scoring 15 goals and registering three assists in 12 appearances in all competitions.
Gimenez has 13 goals and three assists in 10 Eredivisie outings, while he has scored twice in one Champions League appearance, helping his side to record a 3-1 win over Lazio last time out in the competition.
The Mexico international has now scored 38 goals and registered six assists in 57 appearances for Feyenoord since making the move to the club from Cruz Azul in July 2022.
A number of clubs, including Real Madrid, Tottenham Hotspur, Chelsea and Arsenal, are said to be keen on the forward, who has another four years left to run on his current deal.
However, Feyenoord will allegedly refuse to sell the striker unless they receive an offer in excess of £87m, which would be a record sale for the Eredivisie.
According to ESPN, Barcelona have now joined the race for the Mexican, but the Catalan outfit are aware that they could be priced out of a move for his signature.
The report claims that the La Liga champions have sent a number of scouts to monitor his performances, and they will continue to 'watch him closely' for the remainder of the season.
FIFA intermediary Morris Pagniello recently claimed that Real Madrid and Tottenham are leading the race for his signature, telling TuttoMercatoWeb: "Now, the teams closest to him are Real Madrid and Tottenham."
However, Gimenez then took to social media to insist that the comments have come from 'sources far from his environment'.
Athletico Paranaense forward Vitor Roque will join Barcelona either in January or next summer, but the club are also looking for a long-term replacement for Robert Lewandowski.
The 35-year-old has again been in strong form this season, scoring six goals and registering four assists in 11 appearances, while he has another three years left to run on his contract at Camp Nou.
However, a host of Saudi Arabian clubs are believed to be keen on the Poland international, and there have been claims that he could move to the country in the latter stages of his career, with Gimenez seen as a potential replacement for him in the future.