The Catalan giants have made securing the midfielder's signature their top priority this summer, with the Arsenal skipper having been strongly linked with a return to his roots for some time.
The Spain international is reported to have told Gunners boss Arsene Wenger that he wants to move on, despite being contracted to the club until 2015.
The issue at present is that Arsenal are reluctant to part with their prized asset, well aware that losing their captain would represent a sizeable step backwards.
An outrageous offer could force their hand, as they could pump the funds back into the team, but they are prepared to hold firm until they get what they want.
Barca, though, have made it clear that they are not prepared to pay over the odds and will look elsewhere should the Gunners refuse to play ball.
A tentative enquiry has already been made in an effort to determine Arsenal's stance, but Laporta admits his club will not be held to ransom in their pursuit of Fabregas.
"We will not sign any players for above market value," he said.
"We are interested in signing Cesc and Arsenal know that but we will not pay an exorbitant price for any player.
"When it comes to market prices, we'll strengthen where we can but will not pay an unrealistic price"