The six-time Ballon d'Or winner is now a free agent after his deal at Camp Nou expired on June 30.
According to reports, Messi has agreed a new five-year deal with the Blaugrana while accepting a substantial pay cut – although there has yet to be official confirmation.
Barca's significant financial difficulties are likely to mean other players must leave before Messi – or any of the club's new signings, including Sergio Aguero – can be registered.
Nevertheless, club president Laporta says negotiations are progressing well and is confident there will be a positive update in the near future.
"The professionals are doing their job well," he said. "We are very satisfied with how everything is progressing.
"But you know that it is a special market that requires patience, skill and sometimes some juggling.
"But I think, as the summer progresses, we will be able to give good news."