Laporta is set to leave his post at the end of the month and will be succeeded by former Barca vice-president Sandro Rosell, who was voted in by the club's socios with a huge majority in Sunday's elections.
And the outgoing president says the deal to take Fabregas back to the Nou Camp, where he played before moving to Arsenal at 16, is "on stand-by".
"The negotiation is on stand-by at the moment, in a tense calm," he said.
"The sooner everything is unblocked, the better, but it must be understood that we, as the buying club, want to pay the least (amount) possible, and Arsenal, as the selling club, want to charge the highest possible amount of money."
Having had an initial bid turned down by the Gunners, Laporta hinted that the Catalans will offer more money for the 23-year-old.
"We will try to adjust to the logic of the market, as always," he said.
And Laporta says he will bring Rosell up to speed with developments concerning the midfielder.
"I will speak to him president to president to bring him up to date with some matters, such as transfers and signings," he said.
Laporta has no doubt that a deal will suit all parties at the Catalan club.
"The player wants to come, (coach) Pep Guardiola and (sporting director) Txiki Begiristain have shown me their wish for the operation to go ahead and I presume Rosell will have that same will," he said.