Any deal is likely to be put on hold till after the tournament if no agreement can be found by Wednesday, when the 23-year-old should be given the day off on the eve of travelling to South Africa with the Spain squad.
Barca have indicated they are ready to play a waiting game till the last day of the transfer window in their pursuit of Fabregas.
Focused: Cesc Fabregas (left) doesn't want any distractions during the World Cup
But there is a nagging desire within the Nou Camp for outgoing president Joan Laporta to complete a deal before elections to replace him take place on Sunday.
Reports in Catalonia say Barca technical secretary Txiki Begiristain and director of football Raul Sanllehi are ready to fly into London for face-to-face negotiations in which they will present an improvement on their £29million opening offer of last week.
Arsenal insist their captain is not for sale at any price, though privately it is believed they are now looking for about £60m.
Shooting star: Barcelona will intensify their hunt for Fabregas
If that valuation cannot be chipped away at, a deal is unlikely this week, as the Spanish champions are reluctant to go above £40m. They are prepared to offer players in part-exchange to break the impasse.
Fabregas is reluctant for talks to distract him during the World Cup.
He is set to play in Spain's friendly against Poland in Murcia on Tuesday night and is then likely to be granted 24 hours off before departing for South Africa. Arsenal demand Barcelona double their offer to £60m for Cesc FabregasBarca keep talking the talk as chief Laporta stands firm in pursuit of CescArsenal midfielder Fabregas makes his comeback in Spain victoryARSENAL FC