Hammers boss David Moyes is keen to add another goal-getter to his squad and has a number of irons in the fire, with Flamengo’s Pedro also of interest.
The Premier League side have been holding talks with PSG about bringing Ekitike to the London Stadium.
The talks are still continuing, according to French outlet Foot Mercato, with the figures of a possible deal being discussed.
There remains the possibility that Ekitike could move to Eintracht Frankfurt.
PSG are looking to sign Eintracht Frankfurt striker Randal Kolo Muani, but that discussion is not linked to those being held on Ekitike.
Ekitike has featured just once, for eight minutes, for PSG so far this season.
He struggled to live up to his billing at the Parc des Princes last term with just four goals scored across 32 outings.