The 26-year-old was in excellent form for Girona during the 2023-24 campaign, scoring three goals and registering six assists in 40 appearances in all competitions.
There is currently a host of speculation surrounding the Spaniard's future, with Barcelona thought to be interested, but Leverkusen had seemingly been closing in on a deal.
According to The Guardian, West Ham are now attempting to hijack the transfer, with the Hammers emerging as serious contenders for the midfielder's signature.
The report claims that Julen Lopetegui's side have made a £14m bid for Garcia, who has previously represented Manchester City in the Premier League.
The midfielder played eight times for the Citizens during the 2016-17 campaign, with four of those outings coming in England's top flight.
Staying with West Ham, Atletico Madrid are allegedly emerging as the favourites to sign Hammers defender Nayef Aguerd during this summer's transfer window.
The Morocco international is widely expected to leave the London Stadium in the upcoming market, with Lyon and Rennes both said to be interested, while he is also being linked with a switch to Saudi Arabia.
However, according to The Sun, Atletico are currently at the head of the queue for his services.
The report claims that the 28-year-old is keen on a switch to Wanda Metropolitano, and Diego Simeone's side are currently in negotiations with the centre-back's English club.
Aguerd, who is believed to be valued by West Ham in the region of £35m, has another three years left to run on his contract with the Hammers.
The defender made 28 appearances for his London team during the 2023-24 campaign, while he has represented them on 58 occasions in all competitions since arriving from Rennes in July 2022.
Meanwhile, Los Angeles Galaxy are allegedly at the head of the queue to sign experienced forward Marco Reus on a free transfer this summer.
The German's final match for Borussia Dortmund proved to be last weekend's Champions League final against Real Madrid, with his contract due to expire on June 30.
A number of clubs have since been linked with Reus, but according to journalist Cesar Luis Merlo, LA Galaxy are the clear favourites for his signature.
Merlo claims that senior figures from the MLS club were at the Champions League final and held discussions with the forward's agent after the match.
Reus, 35, is said to favour a move to LA Galaxy over any other team, and a deal could potentially be confirmed in the near future.
The German scored nine goals and registered 10 assists in 42 appearances for BVB last season but is leaving this summer in search of a new challenge at the end of his career.