The 22-year-old is also reportedly attracting interest from Aston Villa, Crystal Palace, Newcastle United, and West Bromwich Albion, but West Ham manager David Moyes is determined to win the race for Eze.
QPR value their prized asset at £20 million.
Moyes is unconvinced by some of his attackers at West Ham. Felipe Anderson and Manuel Lanzini could be offloaded this summer and therefore boost the Scot's summer transfer budget, while Albian Ajeti is expected to join Celtic on loan for next season.
It's hoped Eze, who has shone as a No. 10 for QPR, would strengthen a team that has lacked reliable goalscorers; Michail Antonio and Sebastien Haller combined for only 17 goals in the 2019-20 Premier League campaign. Eze scored 14 goals and assisted eight times in the Championship.
West Ham are "prepared to make the funds available" to sign Eze, Steinberg understands. Crystal Palace have been tracking Eze for some time and are believed to be the Irons' fiercest competitors for the London-born forward.
West Ham could attempt to sign Said Benrahma from Brentford if a move for Eze falls through. However, Benrahma would be harder to acquire if the Bees are promoted to the Premier League via the Championship playoffs.