The 22-year-old midfielder has been tracked by Liverpool manager Rafael Benitez, and the Chronicle claims he is "desperate" to move to Anfield.
But Kevin Keegan is sick of Benitez offering bargain-basement players in exchange for a player who is tipped to become a full England international.
Aston Villa have already offered £7m, and it remains to be seen if they will continue their interest, but the fact Liverpool are not prepared to bid any higher could coax them into a £8m bid.
Benitez puts forward the argument Milner is unproven at European and international level.
And he could wait for Milner to continue making his feelings felt that he wants a transfer to Anfield, obviously putting the ball back in Keegan's court.