Crystal Palace striker Dwight Gayle has four goals in nine appearances this season.
However, the Canaries have continued to track Gayle’s progress, and they are optimistic that they could land the striker in January.
Palace are said to be open to doing a deal for the 25-year-old, but they will only sell if they have a suitable replacement lined-up.
Palace have struggled to find the answer to their striking problem all season, and Alan Pardew is keen to bring in another front-man in the new year.
Norwich, meanwhile, believe Gayle could be their main goalscoring threat, as they look to survive in the Premier League.
Gayle has been Palace’s top-scorer for the last two seasons, since signing from Peterborough United. He has netted four times in nine appearances this term.