Hugill was signed by the Hammers in January 2018.
The 27-year-old has managed 11 goals and one assist in 26 Championship starts and nine substitute appearances. He has also netted twice in two FA Cup games.
But the club are unlikely to make a permanent offer, as he may be too expensive for their budget, according to football.london.
"I'd love to prove myself at a Premier League club," Hugill said earlier this month to Sky Sports.
"It's what every player wants to do, because it is the best. And if the opportunity is there for me, I'd love to take it and prove David Moyes right, and the whole staff there to prove them right for signing me and that it was the right decision to do that.
"For me, personally, that has got to be my aim."