The Hammers are desperate to sign a new striker as soon as the transfer window re-opens and Martins has joined Diego Forlan and Diego Milito as an overseas loan option.
Martins is currently with MLS side Seattle Sounders and could be available for loan during the off-season in America.
West Ham boss Sam Allardyce managed Martins at Newcastle, where the Nigerian scored 35 goals in three years. The 29-year-old has netted eight goals in 22 games for Seattle.
Martins could see a short-term spell at West Ham as being beneficial to his hopes of securing a place in Nigeria’s World Cup squad.
Club co-owner David Gold this week told a West Ham fans’ forum that moves are already being made to secure a January loan signing.
The Hammers missed out on signing Demba Ba, Romelu Lukaku, Loic Remy and Jermain Defoe during the summer and have paid the price for a lack of goals.
Andy Carroll’s injury problems have meant Allardyce has been forced to rely heavily on Modibo Maiga, who has not scored in the Premier League since Dec 1 last year.
Gold admitted to supporters it was a mistake not to sign a back-up for Carroll in the August transfer window.
Captain Kevin Nolan was also at the fans’ forum, along with Allardyce, and apologised for the red card he received at Liverpool that rules him out of the next three games.
Nolan, who cancelled the players’ Christmas party, promised he would be spending his spare time working on his finishing, having netted just once this season.
West Ham face bottom-of-the-table Sunderland on Saturday in the game that has been described as a ‘cup final’ within Upton Park.
The match could be key to the future of Allardyce, with the Hammers due to face rivals Tottenham in the Capital One Cup, Manchester United, Arsenal and West Brom before the New Year.
Allardyce told fans that he has targeted a minimum of six points from the next four games and promised to send out a strong side against Spurs in the Capital One Cup.
Meanwhile, West Ham are planning to stage a party on the pitch to marking leaving Upton Park for the Olympic Stadium at the end of the 2015/16 season.
Supporters are also set to be given the chance to name two sides of the Olympic Stadium after West Ham legends.
The Telegraph (UK)