Dembele, a €105million signing from Borussia Dortmund in 2017, is out of contract at the end of the season and has been linked with a move away from Camp Nou in January.
Recent reports from Spain suggest the France international's agent, Moussa Sissoko, is prepared to listen to offers as he is not happy with Barca's latest contract proposal.
The 24-year-old can discuss a free transfer with overseas clubs from next month if fresh terms cannot be finalised with Barca, but Laporta is hopeful of an agreement being found.
"It has been a slower process than desired on our part," he said. "We are working on it, we continue with our swords raised."
Dembele's time at Barcelona has been blighted by fitness problems, but he remains a key player for the Catalan giants when available.
He has managed 30 goals and 20 assists in 121 appearances since his debut in September 2017, meaning he has been directly involved in 0.65 goals per 90 minutes.
That puts him on a par with Liverpool's Roberto Firmino among players from Europe's top five leagues, and just behind Inter's Lautaro Martinez (0.67).
However, to put Dembele's injury issues into some context, the 121 games he has played for Barca is 91 fewer than team-mate Sergio Busquets over the same period.
Laporta is excited about what Dembele still has to give to Barca, though, should a new contract be agreed.
Dembele's future is one of a number of issues Barca have to resolve ahead of the January transfer window, which is expected to be a quiet one at Camp Nou.
The club's well-documented financial problems mean signing any new players next month is not possible unless others are moved on.
"We can't ignore that there is a salary margin. We first have to expand that salary margin and the only way to expand it is for some players to come out of the squad," Laporta said.
"Xavi knows the players he has and is in permanent communication with the football director, Mateu Alemany, our general director and the people we trust.
"If it is possible to strengthen the team, we will see what possibilities we have.
"Xavi has a lot of players and we are sure that he will be able to get much more out of the squad than has been obtained so far.
"We are confident that Xavi will apply a criterion that will make this squad much more efficient than it is."
Barca is unbeaten in three games under new head coach Xavi and return to LaLiga action on Sunday (AEDT) with a home match against Real Betis.