The 22-year-old has elevated his game to new heights since joining the Dutch outfit from Mexican club Cruz Azul in the summer of 2022, scoring 43 goals in 67 appearances across all competitions.
After netting 28 times in 50 games during his first season at the club, Gimenez has since made an electric start to the current campaign, scoring 20 goals in 22 appearances, including 18 strikes in just 16 Eredivisie matches.
Gimenez still has over three years remaining on his contract with Feyenoord, but the striker's exceptional form in front of goal has led to speculation over a possible move to a top European club.
Indeed, La Liga giants Barcelona and Real Madrid are both believed to be interested in the Mexico international along with Premier League sides such as Arsenal, Chelsea and Tottenham Hotspur.
According to The Times, West Ham are the latest club to be 'tracking' Gimenez as they weigh up bolstering their attacking options in January.
However, the report adds that Feyenoord are hoping to fend off interest from potential suitors until the summer.
Gimenez is said to be valued at around £30m and the striker would want to be assured of regular first-team football if he were to leave Feyenoord and continue his promising development.
West Ham delved into the Eredivisie market to recruit two players last summer in the form of Edson Alvarez and Mohammed Kudus, spending in excess of £60m to sign the pair from Ajax.
However, Kudus is one of a number of attack-minded players currently unavailable for Hammers boss David Moyes as he is representing Ghana on international duty at the Africa Cup of Nations.
Moyes is also having to cope without Michail Antonio and Jarrod Bowen due to respective knee and ankle injuries, while Lucas Paqueta is facing six to eight weeks on the sidelines with a calf problem.
In addition, the futures of Danny Ings and Said Benrahma, who have both struggled for regular first-team football this season, are believed to be uncertain amid interest from other clubs.
West Ham have therefore been tipped to bolster their squad in the attacking department before the January transfer window slams shut, with Gimenez one name said to be on the club's radar.
The Hammers have also been credited with an interest in Stuttgart's star striker Serhou Guirassy, who has scored 19 goals in just 16 appearances for Stuttgart this season and reportedly possesses a €17.5m (£15.2m) release clause in his contract.