Liverpool boss Roy Hodgson is keen to bring in Parker as an replacement for Javier Mascherano, who is closing in on a £20million move to Inter Milan.
West Ham have insisted all summer that they have no plans of selling Parker.
“Not at any price,” said chairman David Sullivan.
Tottenham are also keen on signing the midfielder, who Liverpool are ready to make an £8million bid for, according to the Sunday Mirror.
