The Finland striker has scored nine goals and provided three assists this season but is unavailable for selection due to a hamstring strain. Farke expects the striker to return for Norwich’s match with Bournemouth on Saturday 18 January.
Though Norwich are seven points from safety and find themselves rock bottom of the Premier League, Farke spoke of wanting his side “to be brave” at Manchester United.
“I want us to stick to our philosophy,” he said. “They have some world-class players but I want us to be the protagonists.”
The German manager also confirmed that Timm Klose and striker Josip Drmic are out, though Ralf Fahrmann is fit and Godfrey is nearing a return. “He’s doing everything he can in his rehab,” Farke said. “He [Godfrey] has a chance to join us at any point next week.”
With both Drmic and Pukki unavailable, 18-year-old Irish striker Adam Idah is expected to start at Old Trafford, building on his impressive hat-trick in the Canaries’ 4-2 FA Cup third round victory over Preston North End last Saturday.
However, Farke also did not rule out loaning out the youngster this month and, should he leave Carrow Road, he would become the second departure after Dennis Srbeny.
The German forward rejoined former club Paderborn on Wednesday, though Farke admitted “in an ideal world, we would have waited until after the United game”.
The 43-year-old manager also touched on Norwich’s links to Hertha Berlin midfielder Ondrej Duda saying: “We’re looking to strengthen and bring in some options. I think we need a few more options. Duda, we know this player and he is a good player without any doubt. Let’s see how the next days develop.”
Farke also warded off interest in young full-back Max Aarons, who is linked with a lucrative move to Germany, saying: “I wouldn’t spend too much energy listening to all these rumours. Listen, Max is a young guy, only 20 years old and he has four years on his contract.
“It’s not the right time for him even to think about a January move. If I am honest when you see so many clubs linked with him you have to be very doubtful.
“In Germany a few days ago they say he had already signed for Bayern Munich, then the next day it is Borussia Dortmund. Here in England rumours each and every top club want him.
“When so many clubs are in the race it is very doubtful if that is the case. He has a long contract here and he’s totally at the right place. I think he has played something like 21 Premier League games so far, leave him alone and let him play his football.”