The 22-year-old has been a key player under Kevin Keegan, scoring in the 3-2 Carling Cup win at Coventry on Tuesday.
However, having been linked with Aston Villa all summer, it appears Milner has decided his future lies elsewhere.
"We have yet to receive an offer for James that matches our valuation," read a club statement.
"The club is very disappointed that James sees his footballing future as being away from St James' Park. He is a valued member of the squad and it is only a year ago that he signed an improved long-term contract here."
Newspaper reports claimed on Wednesday that Villa boss Martin O'Neill was preparing a £9m offer for Milner.
Milner was on the verge of joining the Villans in August 2006 for around £4m after a lengthy spell there on loan, but Newcastle pulled out of the deal at the 11th hour at the end of the transfer window.
Liverpool have also been linked with a move for Milner, who signed a new four-year contract at St James' Park only last year.