Montero, who was recently on trail at Real Betis in Spain, has netted nine times in 15 games for Seattle, and reportedly has caught the eye of the London club.
Roy Hodgson now has to replace Bobby Zamora, who has signed for Hull City in an $8.2 million deal. This money will give Hodgson valuable funds with which to bolster his attack.
Earlier reports suggested Fulham was in the hunt for Swedish hitman Marcus Berg. However, the Cottagers' interest appears to have fallen short as it now seems likely that the Swede will pen a contract for German side Hamburg over the course of the next 24 hours.
Montero, who has three international caps to his name and has scored one goal for his country, has also been linked with several other Premier League clubs.