The Premier League side are considering going after the 34-year-old who has previously hinted that he wants to move to England at some point.
The 34-year-old is planning to leave Parc des Princes at the end of the season, and has previously hinted that he would be interested in moving to the Premier League before the end of his career, The Sun reports.
The Sun adds that while West Ham are unlikely to be playing in the Champions League next season - unless they manage to claw back the seven point gap that separates them from the top four - they are already plotting a potential deal, and are willing to give the Sweden international a contract that would see him earn £120,000 a week.
While Ibra is in the twilight of his career, his form in recent years suggests that he would still be an incredible signing for the Hammers.
Currently, the former Barcelona and Juventus forward leads the Ligue 1 goalscoring charts, as his tally of 23 goals in 21 games leaves him 10 strikes clear of Michy Batshuayi, who is also on West Ham's radar (via The Sun).
And with Slaven Bilic's side moving into the Olympic Stadium next season, signing a player of Ibrahimovic's calibre and reputation would send an enormous message about the direction the club feels it is going in, especially if the maverick forward has a similar impact to the last player that the Irons signed from the French league, Dimitri Payet.