Sky Sports sources understand Chelsea have increased their bid for Tottenham's Luka Modric to £27million.
Last season's Premier League runners-up have been expected to make an improved offer for the Croatia international since failing with a £22m approach in mid-June.
Having lost Michael Essien for up to six months due to knee surgery, Chelsea, under the management of Andre Villas-Boas, have now made their latest approach with a £5m increase on their original offer.
Modric has said he may request a transfer in order to move to Stamford Bridge, but Tottenham chairman Daniel Levy has already made it clear that the 2008 signing from Dynamo Zagreb will not be sold.
It therefore seems unlikely that the £27m will be accepted and earlier on Monday evening Spurs manager Harry Redknapp described the previous £22m offer as a 'joke'.
Redknapp, though, has acknowledged that Levy makes the final decisions regarding transfers and the White Hart Lane boss has also admitted the need to sell in order to bring new players into his squad after the failure to qualify for the UEFA Champions League.
Speculation has suggested that Lyon's £9m-rated Bosnian, Miralem Pjanic, is being considered as a potential replacement, but it was also reported over the weekend that Tottenham were preparing a new £80,000-a-week five-year contract offer for Modric.
The deal would make the 25-year-old Tottenham's highest-paid star, but the player's threat to request a transfer means it appears impossible for Levy to convince him he has a future at White Hart Lane.
Modric, who could potentially earn £120,000-a-week at Chelsea, has already claimed that Levy has betrayed a gentleman's agreement which was struck when he signed a new six-year contract worth £50,000-a-week in May 2010.
Levy insists no such agreement exists, but Modric believes there was an understanding that Tottenham would listen to offers from perceivably bigger clubs.
Where will Luka Modric be playing next season?