The Nigerian ace spent the 2010/11 season with the Hammers, smashing in eight goals before returning to Inter Milan.
Since heading away to Italy, Obinna has moved to Lokomotiv Moscow but his spell in Russia looks set to come to an end soon.
The 27-year-old has found it difficult to settle at his current club, and is rumoured to be ready to follow up a loan move to Chievo from the latter half of last season with a permanent switch to one of Europe’s more established leagues.
Hammers boss Sam Allardyce is desperate to bolster his forward line in the coming months, and is tempted by partnering the pacey Obinna with Andy Carroll.
The African star was a fans’ favourite during his brief spell in east London, and a move to bring him back could ease tensions between ‘Big Sam’ and sections of the Irons’ support.
The versatile attacker is set to represent Nigeria at the World Cup this summer.