"Bids are only bids if someone has sent you a fax with a concrete offer, and I have not had one of those for Billy, or any of our players for that matter," Fitton told the Swindon Advertiser.
"I've heard and read about a lot of clubs who are supposedly interested in Billy, but none of them have got in contact with me. Billy is very much part of our plans going forward, and I have never doubted that he wants to stay."
Paynter, whose representatives are in talks with Fitton over a new contract, added: "I want to stay here. I believe the club is on a high and going forward."
Meanwhile, Simon Ferry, who recently extended his loan until the end of the season, is keen to join the club on a permanent basis. He said: "At the moment, nothing's been spoken about staying any longer than the end of the season. You never know what's going to happen at either club, but it's something that I would love to do."