Fulham boss Roy Hodgson has already hit out after Baggies chairman Jeremy Peace labelled the Barclays Premier League club’s first offer for Greening – £2m plus a player – as “derisory”.

He was further disheartened when Albion turned down a second bid of £3.25m on Monday.

Today’s developments leave the saga at a crossroads, with Hodgson facing a decision over whether to again up the bid or start looking elsewhere.

Greening has made it clear he will happily remain at The Hawthorns if an offer does not come in that matches the club’s valuation.

West Brom have themselves seen a bid rejected by Coca-Cola Championship neighbours Coventry for Danny Fox – with the left-back now understood to be close to joining former Baggies boss Tony Mowbray at Celtic.

Albion put a package deal valued at just below £2m on the table, but that was turned down by the Sky Blues, ending the club’s interest in the defender.

Meanwhile, Baggies left-back Marek Cech has stressed his determination to resolve his future as soon as possible.

The Slovakia international has attracted interest from Celtic and Dutch side FC Twente, according to his agent, although West Brom are keen to retain his services.

Cech made just eight league appearances last season, but the exit of fellow left-back Paul Robinson to Bolton and Mowbray to Parkhead could see him back in the frame.

Cech is also wary of the effect Albion’s relegation will have on his chances of making Slovakia’s squad for next year’s World Cup in South Africa.

He told the Birmingham Mail: “At this moment we are discussing things.

“We will see in the next few days how my future will pan out. I can’t say now whether I’ll stay or go.

“We will see what the decision is – it may take a few days, maybe a few weeks.

“If it’s decided I stay then I will take it professionally. But these are things I need to consider before a decision is made.”