West Brom have rejected a second offer from Fulham of £3.25million for captain Jonathan Greening.
The Baggies midfielder handed in a written transfer request earlier this month, stating his desire to have another crack at the Barclays Premier League before the chance passes him by as the underlying reason.
Greening has promised he will "in no way want to rock the boat" should a suitable offer not come in for his services.
Fulham's opening offer was swiftly rejected last week with Albion chairman Jeremy Peace labelling the bid "derisory".
Roy Hodgson was understood to have offered £2million plus a player, and his latest attempt to prize the 30-year-old away from The Hawthorns shows he is still keen.
Albion, who do not want or need to sell, value Greening higher than the two bids received and it remains to be seen whether the Cottagers will come back in for a third time.
The former Manchester United and Middlesbrough man still has a year left on his current deal with another 12 months in West Brom's favour, while a new four-year deal is also on the table.
Hodgson, who defended Fulham's opening bid, last week said: "I do know that Jonathan will be very keen to join us and he will be a good addition to our squad with his experience and quality going into the season we're going into."
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