The Hammers are reportedly flirting with the idea of signing the goal machine.
In February, the Hammers were linked with a sensational swoop (The Sun) for the Paris Saint-Germain marksman, who is expected to leave the French capital at the end of this season when his contract expires.
Earlier this week, his agent Mino Raiola fuelled speculation linking him with a switch to England by confirming that a host of English clubs have "knocked on the door" enquiring about the former AC Milan and Barcelona hitman (The Mirror).
The Irons co-chairman David Sullivan told talkSPORT recently that he'd love the 34-year-old; sentiments which goalkeeper Adrian shares, noting that he could be next season's Dimitri Payet in East London.
"He's a great player, a star who has won titles everywhere. If he comes to add (something extra to the team) he will be welcomed," the keeper said to Spanish news agency EFE, as quoted by IBT.
"This season arrived Dimitri Payet and it is very nice that players of that level come (to West Ham). If the president is aiming to reach those levels, is great."
As exciting as it is for West Ham fans, you do wonder how realistic the move actually is, with Ibrahimovic's mega-money wages likely to mean the Hammers may be trumped by bigger clubs.
Still, it is free to dream and although Ibrahimovic may not happen, manager Slaven Bilic has certainly made the Irons a much more exciting proposition for future signings.