The defender, who arrived from Burton at the start of the season, has attracted plenty of suitors following his solid debut campaign for Alex.
Derby, among others, have emerged as serious contenders for Brayford's signature with Thordarson recently insisting he would not be sold on the cheap if recently-relegated Crewe did have to part ways.
Brayford himself has admitted he would be more than happy to stay but recognised the situation could be taken out of hands. Yet Thordarson has revealed all is currently quiet on that front, much to his delight.
The Alex boss told the club's official website: "Nothing has happened with John Brayford. Since the season ended it has gone a little bit quiet but we will see what happens.
"I'm sure there will be clubs out there assessing their options and I still expect someone to come in and make us an offer. I would be delighted if John stays with us because he is one of our best players and had a terrific season for me."