The Hammers are on a drive to improve their attacking options, and the 29-year-old former Manchester United and Real Madrid striker might be the perfect solution.
Chicharito scored 13 goals in 36 games in all competitions for the Bundesliga side last term following his 26 goals the previous year.
Leverkusen sporting director Rudi Voller has now given the clearest indication that the club would be open to selling the Mexico international, who could reportedly join West Ham for £13million, as he enters the final year of his current contract.
Voller told Frankfurter Allgemeinen Zeitung: “He’s interesting to many parties because of his quality.
“We often receive enquiries.
“We can wait a little. Something can happen later on.”
Voller, however, said the club would not be selling goalkeeper Bernd Leno, who is wanted by Napoli.
“He is the clear number two in Germany. Napoli asked, we had contact, but we said very clearly: no chance.”