MIDDLESBROUGH are understood to have opened the bidding at £3m for Geremi - and been told by Real Madrid to double the money.
Real have confirmed that Boro have lodged an offer for the Cameroon international, who has been a huge success during his season-long loan at the Riverside.
Midfielder Geremi, 24, has indicated his willingness to make the move permanent, as long as he can agree personal terms.
Real's asking price, initially £9.6m, could be the stumbling block.
But Northern Echo Sport understands that Real are likely to accept an offer of around £6m.
Boro plan further talks with the European champions and are hopeful that they can agree a compromise deal.
Boro boss Steve McClaren, meanwhile, has warned title-chasing Arsenal that his side will play without fear in Saturday's Riverside clash.
The Teessiders are unbeaten in eight games following the goalless weekend visit to Manchester City.
McClaren said: ''We're on a tidy run at the moment and we've found what we've been striving for all season - consistency.
''Maybe we should have won more games, but not losing breeds confidence and the way we're playing, we should be looking forward to Arsenal coming here. There is definitely no fear involved in facing them.
''We know we have a good team. You can see that in the way we pass the ball, control the ball and defend, and it's important we keep that run going.''
l Boro duo Brad Jones and Luke Wilkshire have been named in the Australia Under-23 squad for the game in Spain in a fortnight.
l Middlesbrough, winners of only two of their previous nine visits to the Hawthorns, suffered a customary defeat when they paid the penalty for some weak finishing, going down 1-0 to West Brom, writes NEIL ANDREWS.
They produced some attractive attacking play with Luke Wilkshire prominent.
Jamie Cade hit the woodwork in the first half following a Wilkshire free kick, while Albion posed few problems for the Boro defence in which David Murphy and Chris Riggott shone.
It was a big surprise when Albion went ahead in the 40th minute with a powerful shot from Danny Carey-Bertram which was deflected into the net.
In the second period Boro swamped Albion's defence and goalkeeper Brian Jensen was tested by Stewart Downing and Craig Dove.
Cade wasted Boro's best opportunity when he had a free shot from 18 yards only to fire wide.
Boro: Jones, Stockdale, Murphy, Smith, Riggott, Vidmar, Wilkshire, Wilson, Cade (Graham 62), Dove, Downing. Subs (not used): Roberts, Van Kanten, Garbutt.
Read more about Middlesbrough here.
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