Rams boss Nigel Clough is keen to sign the 21-year-old defender, who was Crewe's player of the year following his move from Clough's former club Burton in September.
Thordarson insists there are three clubs interested in signing Brayford and that the right offer would see him exit Gresty Road.
"I don't want to lose John but, in reality, if the right offer comes in for us and for him then he will move on to bigger and better things, if he is comfortable with the deal," Thordarson told the Sentinel.
"There is interest out there in John and the market will take care of itself. We had an offer from Derby and, as yet, that is the only offer we have had. Three clubs are interested but it is still early in pre-season.
"John is a top man and I have enjoyed working with him. He has applied himself since he came here and the industry knows what type of character he is. I am not surprised clubs have an interest in him because he is a good character and a good player."