Gary Megson was reported to have made a £100,000 offer for the forward, who is out of contract in the summer but Swindon deputy chairman Mark Devlin commented: "I've read about Forest's supposed interest in the newspapers but we've had no official bid.
"By that I mean that we have received nothing in writing.
"I'm not surprised that Rory is being linked with other clubs because he is playing well and scoring goals.
"But we are desperate to keep him here and as everybody knows, we've been talking about a new deal."
23-year-old Fallon has scored 12 goals this season for struggling Swindon.