The Catalan giants are keen to strengthen their defense, having missed out on Thiago Silva for the second summer in a row, but have been told to up their offer for the Blues star
Such a fee would represent a new high-water mark for a defender, exceeding the £37m that Paris Saint-Germain paid to beat Barca to the signature of Thiago Silva last year. The Spanish champions have spent the entire summer attempting to solve the problem left by that transfer-market failure.
The Blaugrana initially attempted to recruit Thiago Silva again, only to be rebuffed by PSG, and the subsequent bid for Luiz – with £17.2m guaranteed and a further £4.3m dependent on performances – was less than the 26-year-old's purchase price from Benfica and was quickly rejected.
"If they need a central defender my advice is that they have to go to the second name they have in the list because they are wasting their time," said Mourinho after the offer became public. While Barcelona is ready to increase the sum to £21.5m plus variables, Chelsea will not sell at that level.
The Catalans have looked at two other Premier League defenders as alternatives, making an enquiry over the availability of Jan Vertonghen with Tottenham and placing a bid with Liverpool for Daniel Agger. Neither move has been well received.
Spurs expect to lose Gareth Bale to Real Madrid, so they have no interest in selling a defender who excelled in his first season in English football, scoring seven goals in 48 appearances and being named in the Premier League's Team of the Year.
Vertonghen is aware of Barcelona's interest in signing him and, according to a friend, has long held an ambition of playing at Camp Nou. He has, though, enjoyed his first year at Tottenham and is thought unlikely to push for a transfer in the manner that Bale has.
Liverpool flatly rejected Barca's proposed £5.1m transfer fee for Agger, a player who was close to moving to Manchester City for several times that amount 12 months ago.
"We are aware that Barcelona have made an offer for Daniel that Liverpool have rejected," said the Dane's agent, Per Steffensen. "Daniel has a contract with Liverpool for the next three years and it would be up to the clubs to agree a fee for his transfer in order for that to change."
Barcelona's already problematic finances have been further strained by the huge sums to committed to keeping Neymar out of the hands of Real Madrid. If a deal remains impossible to agree for one of the team's three Premier League targets, the club may turn to France international Mamadou Sakho, who has been relegated to reserve status at PSG.
Follow Duncan Castles on