The 29-year-old has been on loan at Carrow Road since the summer, scoring two goals in seven appearances to date. And that form has seemingly convinced Norwich that he can be a long term option at the club.
Jarvis has recently been side-lined with a twisted knee, but despite missing the last six Premier League games Norwich have reportedly made their move.
The Mail claims Norwich have offered Jarvis a four and a half year contract with West Ham set to take a sizeable hit when you consider how much they paid for the wide man back in 2012.
The Hammers paid Wolves a then club record £10.75million for Jarvis but in the intervening years he has scored just six goals and provided nine assists in 90 appearances.
That is not exactly the return West Ham will have hoped for, but he has offered enough on loan to suggest he could excel at Norwich for the next few seasons.