It had been reported that the 24-year-old left-back had completed a free transfer move from Scunthorpe. However, both clubs have denied that anything has been signed.
Iron manager Brian Laws said: "I know absolutely nothing about it. I have a lot of respect for Andy Dawson and he has a lot of respect for me and the first port of call if he ever moves will be to my door."
Meanwhile, City say that no signings are expected to made before the end of next month when players reach the end of their contracts.
Dawson is thought to have travelled with the rest of the United squad on their end-of-season holiday.