The Lilywhites have had no approach or contact from their fellow Championship club regarding Grayson who is the bookies’ favourite for the Stadium of Light vacancy.
Pre-season training starts on Thursday and the timing of the speculation is not the best.
But it has not stopped things carrying on as normal at North End.
Recruitment is ongoing, with more deals to be done to add to the summer arrivals of Declan Rudd, Sean Maguire and Josh Harrop.
Preston have been dragged into a saga at Sunderland which is now in its fifth week.
It all started with David Moyes’ resignation as Black Cats boss after relegation from the Premier League.
Grayson was in the betting from fairly early on, briefly the favourite last month but Derek McInnes at Aberdeen was the man who Sunderland initally wanted.
When he turned the job down, Grayson’s name went to the top of the bookies’ odds.
However, Sunderland then put their managerial search on hold while talks were held over the possible sale of the club by owner Ellis Short.
A German consortium is in the running to buy them and if their bid succeeds, they want to put a German coach in charge – Jurgen Klinsmann and Jens Keller are two names to be strongly linked.
If the sale doesn’t go through and ownership stays with Short, that is where the Grayson link is.
The North End manager is reported to be the current Sunderland board’s choice to succeed Moyes.
So until the Wearsiders sort out the ownership issue, little can progress on their search for a new boss.
If the sale to the German consortium goes through, it would make the speculation over Grayson irrelevant.
But if Sunderland stays in the current owner’s hands, that would put North End on alert for a possible approach.
As well as McInnes, others have previously been in the frame for the job – Nigel Pearson and Chris Wilder two names to feature prominently.
Grayson has been Preston boss for four years and four months, the longest-serving manager at Deepdale since the 1960s.
Meanwhile, former PNE youngster Nick Anderton has joined Blackpool from Barrow in a £75,000 deal.
Anderton, a left-back, was freed by Preston last summer after two years on the books as a professional – he was in the youth team previously.
He joined Barrow and some impressive performances for the Cumbrian outfit last season in the National League caught the attention of several clubs.