Sevilla have told Chelsea and Jules Kounde's other suitors that they must meet the defender's reduced asking price within a week or face paying a significantly higher fee, 90min understands.
The centre-back remains a transfer target for the London club but they are prioritising their pursuit of Juventus' Matthijs de Ligt, having been alerted to the Dutchman's potential availability amid his contract impasse.
Barcelona have emerged as rivals for Kounde's signature, although sources have told 90min Chelsea are unconcerned by their interest having played the long game to get to the front of the queue. The Frenchman's desire to move to London is also unwavering having come close to joining the Blues last summer.
Sevilla had previously been demanding a fee close to the France international's €80m release clause, but they have softened their stance in recent weeks and would now accept a figure in the region of €60m.
However, while Chelsea have maintained contact in the past week, a suitable offer has not been forthcoming - and 90min understands Sevilla intend to bump their asking price back up unless someone stumps up the money by Tuesday 5 July.
That is when the Rojiblancos return for pre-season training, and sporting director Monchi wants the transfer to be wrapped up by then. If that is not the case then Sevilla will once again demand something closer to Kounde's release clause.
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Chelsea's negotiations for the France international have dragged on, and 90min reported earlier this month that the 23-year-old's representatives are growing frustrated with a perceived lack of effort to get the deal done.
As well as De Ligt, the Blues have also enquired about versatile Man City defender Nathan Ake - who is free to leave the Etihad Stadium - and Napoli's Kalidou Koulibaly, while they are expected to meet with Torino regarding Gleison Bremer. New owner Todd Boehly keeping the club's options open as they seek defensive reinforcements.
Source : 90min