Sky Sports says the Hammers have opened talks with their London rivals to ease their attacking crisis, with Andre Ayew, Andy Carroll and Diafra Sakho all currently sidelined due to injury.
Club boss Slaven Bilic said on 24 August that he would try to complete moves for Manchester City's Wilfried Bony and Juventus forward Simone Zaza before the end of the transfer window.
Chelsea are reported to favour a permanent move for Remy, who has not featured in any matchday squad so far this season under new manager Antonio Conte.
Spanish club Valencia are also interested in signing the Frenchman, while Crystal Palace have made enquiries about the player in the past, according to Sky.
Remy, 29, joined Chelsea from Queens Park Rangers in January 2014. He made 13 league appearances for the Blues last season, scoring one goal, and has two years left on his Stamford Bridge contract.
Speaking ahead of the Europa League qualifier second leg against Astra Giurgiu, Bilic confirmed that he was interested in both Bony and Zaza.
"[Bony] is an option, because he plays the position that we've tried to sign a player, even before the injuries," he was reported as saying by the club's official website.
"[Zaza] is a top player, I like him, and I was here last year so it tells you everything.
"We were in contact with him last year, it didn't happen, we will see this year."
However, the 47-year-old insisted that any new arrivals would be long-term acquisitions rather than stop gap measures.
"We are not going to sign someone just because we have to act now. The longest injury we have is Ayew and we expect him to be fit by December 1," he said.
"We have to be optimistic and cannot moan about the situation because that does not help.
"We will do something if we can in the next few days, without panicking and that is exactly what we are doing."