Maddison has arguably been the Canaries' best player this season. The 21-year-old currently tops the club's scoring charts in the Championship alongside Nelson Oliveira, having scored seven times, while he is out in front by quite some distance when it comes to assists, having contributed five this term.
However, the Guardian adds that Norwich are looking for more for the former Coventry City ace - who David Moyes watched when Daniel Farke's men took on Chelsea in the FA Cup - so it seems highly likely that the Hammers' bid may be rejected.
It remains to be seen whether West Ham plan to return with another offer during this window. It may certainly prove a good idea to try and get a deal done this month.
If Maddison enjoys a strong second half of the season, his value may rise significantly. And given the interest in him from the likes of Spurs and Liverpool, West Ham may perhaps be taking a risk if they decide to hold fire on a move until the summer and not make another bid before Wednesday's deadline.