Fabregas started his career in the Barcelona youth ranks before being lured to north London in 2003.
The 23-year-old has flourished at Arsenal, taking over the club captaincy, and has also racked up 50 caps for Spain.
Barca have already had an initial bid - thought to be in the region of £29million - rejected by Arsenal but Laporta believes the Gunners will not be able to keep hold of their talisman beyond the summer.
"Arsenal will end up giving in, but I don't know when that will be. We will have to wait and let the professionals who are taking care of it do their work," he told reporters on a visit to Sant Guim de Freixenet.
Laporta is set to leave office at the end of the month to be replaced by president-elect Sandro Rosell and is unsure whether a deal can be struck before then.
"If it's not us, it will be up to the new board, if they consider if appropriate, to carry on along this road," he told Barca's official website.
Barca have already signed Spain striker David Villa from Valencia this summer and have been linked with a move for his international team-mate Fernando Torres.
That means both Zlatan Ibrahimovic and Thierry Henry could be set for summer exits.
"The market is very changeable and is moving at the moment, so we have to be careful in that sense," said Laporta, who revealed Henry's future will be decided "when the World Cup finishes for France".