The European champions have been chasing the Spain international for two years and the midfielder is himself thought to want to return to his boyhood club.
Arsenal have already rejected a £26million bid from Barcelona for Fabregas this summer, while the English club's chairman, Peter Hill-Wood, has also said another 'tentative' offer has been unsuccessful.
Fabregas is thought to be valued at a minimum of £40million by Arsenal, but Barcelona's next offer is reportedly set to be worth just £27million - a figure that is unlikely to tempt The Gunners into doing business with the Nou Camp outfit.
But, having already signed Chile star Alexis Sanchez from Udinese in July, Barcelona manager Guardiola has offered a less than subtle hint that he is still determined to complete a deal for Fabregas.
Guardiola is quoted as saying in the Daily Telegraph: "We're short of just one player and everyone knows which one that is."
The loss of Fabregas would come as a bitter setback for Arsenal fans, who at the weekend booed their team from the field following a 1-1 draw with New York Red Bulls.
Manager Arsene Wenger's failure to complete a major signing in the transfer window has been another cause for complaint, despite the interest in Valencia's Juan Mata, Everton's Phil Jagielka and Blackburn's Chris Samba.
And Hill-Wood has explained: "As Arsene said, we are looking to buy some players, but we are not going to do our business in public."