Arsenal rejected a formal offer from the Spanish champions earlier in the week, which Laporta said was for 35 million euros.
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"We consider it to be the market price. Arsenal have rejected it. Now our technical staff should decide what the next step is," Laporta was quoted as saying on the club website.
"(The communication channels) remain open. We are confident Arsenal will end up understanding the situation.
"(The best thing for Fabregas) would be to have the transfer completed as soon as possible, before the start of the World Cup, " he said, while adding, "it is Arsenal's right to stand firm and we respect that."
Laporta was asked if Fabregas might invoke article 17 of FIFA's transfer regulations, the Webster Rule, which allows players under 28 who have served three years of a contract, to "buy out" the remaining time on long-term deals.
"I'm not sure if Cesc would consider that, but we want to reach an agreement by talking to Arsenal," he said.
Fabregas, who returned to action with Spain in a friendly against South Korea on Thursday after two months out injured, signed an eight-year deal with Arsenal in 2006.
The 23-year-old told manager Arsene Wenger he wanted to return to Barca, the club he left for Arsenal aged 16, before joining up with the Spain squad for the World Cup finals.
Arsenal said on Wednesday they would not enter into any negotiations with Barcelona for their captain.
Barcelona are in the middle of a presidential election campaign to find a replacement for the out-going Laporta, with polling day to held on June 13.
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