Newly promoted club Leeds United and Premier League sides West Ham United and Crystal Palace are all locked in a battle to sign Eze who is regarded as the most naturally gifted player outside the English topflight.
Tottenham have also been tracking the 22-year-old who scored 14 goals and provided 14 assists last season.
Bosses at QPR are resigned to the fact that Eze has played his last game for the club and know they will not be able to stop him playing Premier League football.
When West Ham signed Jarrod Bowen from Hull in January they paid £20m and given his success at the London Stadium since then they feel that kind of figure is where bidding should start.
The club now hope there is enough competition for Eze to help spark a bidding war which would drive up the fee.
Leeds want playmaker Eze to lead their return to the Premier League.
Marcelo Bielsa has identified the exciting England Under-21 international as the creative spark his team will need next season.
Sunsport reported that Leeds first declared their interest in Eze in January and told QPR that they would come in with a firm bid if they were promoted.
Now they are preparing to fulfil that promise when the transfer window officially opens next Monday.