Mats Hummels is flattered to be attracting interest from over Europe but has no intention of leaving Borussia Dortmund.
If Danny Rowe departs Rotherham again this season it will only be to Wycombe, according to Millers boss Steve Evans.
Grayson succeeds Graham Westley in the Deepdale hotseat after the ex-Stevenage manager stepped down to end an unsuccessful 13 months at the helm last week, having won just once in npower League One since November.
North End bounced back to defeat leaders Bournemouth 2-0 at the weekend under the guidance of caretaker John Dreyer, but lie 17th in the table, eight points above fourth-bottom Oldham, who have a game in hand.
Grayson was dismissed from his post at Huddersfield last month, despite securing promotion to the Championship last season via the play-offs.
He also lifted Leeds out of the third tier during his time at Elland Road, having accomplished the same feat during his first managerial assignment at Blackpool.Grayson will be assisted by Glynn Snodin, who was his right-hand man at both Leeds and Huddersfield.
Dreyer, who arrived in Lancashire as Westley's assistant in January last year, has been retained as part of the backroom staff.
While acknowledging he could have waited for another job at Championship level, Grayson felt the chance to take up the reins as Westley's successor at Deepdale was too good to turn down.
"I got sacked by Huddersfield a few weeks ago, I've had a break and had a bit of a holiday but in that period of time I've been looking to get back," the 43-year-old said.
"I love football, I'm a football man and I got itchy feet.
"I had one or two other opportunities to go to other clubs and had enquiries about going to other clubs, but once I spoke to the owners here I found a club that could match my ambitions as well as me matching theirs.
"I'm delighted to be here, I know that the club's got a fantastic tradition and history and hopefully we can get back to those winning ways and take the club back to where it belongs in the Championship, and hopefully beyond some day.
He added: "That (waiting for a Championship job) was a possibility but you can wait too long, you can have a breather and be out too long and suddenly you get a little bit forgotten.
"So I thought coming to Preston North End fitted the bill with a lot of things and I'm delighted to have done that.
"If it was a club that didn't have the ambition of trying to be successful then I wouldn't be here but it certainly inspired me to come."