Maddison elevated his status in English football following an impressive campaign for the Canaries in the Championship last season which yielded 15 goals from central midfield.
The England Under-21 star is a known target for Leicester and Everton, as well as Premier League newcomers Fulham - who are keeping tabs on the situation as they look to spend big ahead of their return to the top flight.
With his star continuing to rise Norwich are accepting of the fact that they are likely to lose Maddison this summer so they are hopeful of creating a bidding war after the Hammers' registered as serious contenders.
Following the long term injury to Manuel Lanzini, West Ham have moved to make an official offer for Maddison as he can provide a like for like option in the middle of the park due to his attacking capabilities and eye for goal - as per the Mirror.
Would love this adds free kicks technique pace skills creativity & English rather him then Grealish. And at 21 already brilliant huge potential, love watching him. Tho a lot of clubs keen. But have to fancy first team chances here. Def Pellegrini type for then Moyes. Hope so😍— Joshua (@SchroerJr) June 11, 2018
The Canaries value Maddison in the region of £25m and expect Everton and the Foxes to pose as West Ham's greatest competition to landing the 21-year-old.
The Coventry academy product is on track to recover in time for pre-season after sustaining a knee ligament injury on the final day of last season, a campaign which saw Maddison finish with 44 league appearances as Norwich finished 14th in the table.
Meanwhile the Hammers have also turned to Burnley's Nick Pope as they look to reinforce their goalkeeping ranks at the London Stadium next season, with Lukasz Fabianksi and Jack Butland also being considered as Manuel Pellegrini gets to work on building his own team.