City have been linked with moves for MK Dons' out-of-contract Spanish defender Miguel Angel Llera, Hartlepool defender Michael Nelson and Shrewsbury striker Grant Holt.
Gunn refused to confirm any names of his transfer targets but is hoping to make progress on a new signing very soon.
"There are lots of names cropping up but I am not going to go through individual names and say yes or no," Gunn told the Norwich Evening News.
"There are delicate situations and I don't want to give anything away on who we may be talking to. I have short lists and long lists and there are players coming to the end of their contracts.
"There might be something in the pipeline. We have been speaking to players and players' representatives and are hopeful we can make some announcement in the not too distant future."