According to a report from The Guardian, Remy heads up a list of players Bilic wants as part of his revolution in East London.
The West Ham board are said to be willing to back their new boss with significant funds to bolster a squad that will start the season before any other Premier League side on July 2, when they embark on their Europa League qualifying campaign.
West Ham's woes in the second half of last season - they won just three games in 2015 after their best ever start to a Premier League campaign - can be directly traced to a glut of injuries, particularly to the club's strikers.
The likes of Andy Carroll, Enner Valencia and Diafra Sakho all missed large chunks of the season, which hampered West Ham's progress as the goals dried up.
It is a fact not lost on the former Besiktas and Croatia boss when he analysed the team's performances from last season.
He told West Ham's official website: “They were a little bit unlucky last year with the number of injuries in a crucial stage of the season.
"I definitely think the team can improve, as I said, last year they had some brilliant games, especially in the first half of the season. It will be my job to improve it and make it better."
And it seems the task of 'making it better' could well start in the striking department with the club said to be willing to splash out to make a statement by signing Remy.
The France international, who joined Chelsea from Queens Park Rangers for £8.5m last summer, is said to be restless in West London according to The Mirror, having started just six Premier League games last season.
And the Hammers are hoping the fact Remy will want to play as much as possible to improve his chances of making France's 2016 European Championship squad will work in their favour.
Remy was actually linked with a move to West Ham by The Mirror before he signing on loan for Newcastle United in 2013. He has an impressive ratio of goals since coming to England from Marseille with a total of 27 goals from 63 games.