Just six months ago, some Canaries fans wanted Farke out after a 3-0 home loss to Leeds United in the Championship.
With the German's current deal, signed in May 2017, set to run out this summer, the report says the Canaries want to secure his future at Carrow Road as reward for his work.
Farke's first season with Norwich saw the East Anglian club finish 14th in the Championship table, while earlier in the season, their 3-0 home loss against Leeds United prompted some criticism, as can be seen on the club's Twitter full-time update.
Since then, however, the former Borussia Dortmund II coach has taken his team all the way to the summit after 31 games, including a superb 3-1 win over Marcelo Bielsa's side that led to a switch in positions at the top.
The report goes on to add that negotiations between coach and club have been going on for some time, that progress has been made in the past fortnight, and that Farke's assistant Edmund Riemer is also set to sign.
Norwich's last game saw them claim bragging rights with a 3-0 thumping of East Anglian rivals Ipswich Town and, on Wednesday night, they travel to Preston North End in a bid to maintain their two-point lead over Leeds, who host Swansea City.