West Ham United made an official offer for Stoke City midfielder Joe Allen, but it was rejected.
Football Insidersuggests the offer is somewhere between £5 million and the selling club's asking price of £8 million.
Stoke are open to selling the player in the January transfer window, as he wants a return to the Premier League.
They are not looking like being part of the promotion or playoff race in the second half of the season.
But the Hammers, who are now managed by David Moyes, will have to up their offer to get their man.
West Ham may also look at Genk midfielder Sander Berge as an alternative, as he is much younger and could be available for a similar price.