The Hammers are expected to dip into the transfer market next month in a bid to solve their attacking woes, with ‘Big Sam’ concerned at his lack of options.
Major summer signing Andy Carroll has been unable to make any sort of impact at Upton Park since his permanent arrival from Liverpool, leaving the London club with a somewhat blunt strikeforce.
Jelavic has emerged as a possible solution for Allardyce, with the Croatian set to be allowed to leave Everton next month.
The 28-year-old has failed to hold down a first-team berth under Roberto Martinez, and is thought to be keen to secure regular paying time in the build-up to the World Cup.
West Ham are ready to offer him this, which could tempt the former Rangers man to the capital.
The Irons are also believed to be watching veteran Uruguayan Diego Forlan, while a short-term loan swoop for Seattle Sounders ace Obafemi Martins is also an option.