The 24-year-old striker has been at Pride Park since February.
He has netted twice during a 12-game spell with the Rams and has enjoyed his time in the Championship.
Martin will be out of contract in the summer, paving the way for him to leave Norwich as a free agent.
No decision has been taken on his future as yet, but he would be willing to consider an offer from Derby.
Martin told the Derby Telegraph: "Yes, I'd definitely be open to it.
"I can't really focus too much on it while the season is going on, but I'll be looking to finish strongly and see where that takes me.
"The fans have been great - and the lads as well."