Fulham's improved offer of £3.25million for midfielder Jonathan Greening has been rejected by West Brom.
Greening handed in a transfer request at the Hawthorns earlier this month which was swiftly following by an initial offer from the Cottagers.
The Baggies midfielder has claimed he is eager to have another opportunity to play in the Premier League, but vowed he would not 'rock the boat' if an acceptable offer failed to materialise.
Fulham's opening approach was swiftly rejected last week with Albion chairman Jeremy Peace labelling the bid "derisory".
Roy Hodgson was understood to have tabled £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."