Sporting want roughly €80 million to part with their captain, according to Dawson, who adds the Red Devils are more comfortable paying something in the region of €60 million to procure Fernandes' services.
The Portuguese international, 25, is keen to move to Old Trafford, with super agent Jorge Mendes said to be involved in the negotiations.
Sporting have rejected the opportunity to take goalkeeper Joel Pereira back as a makeweight in the transfer, according to Dawson. They have interest in seldom-used United defender Marcos Rojo, but their efforts to sign him have thus far been spurned.
The two clubs have until Jan. 31 to hammer out a deal.
Fernandes, capped 19 times by Portugal, would provide a much-needed jolt of creativity to Ole Gunnar Solskjaer's languid midfield. He's scored 15 goals in all competitions so far this season, adding 13 assists.