Speaking to Sky Sport at a broadcaster event, Gasperini said pre-season, which begins next Monday, would mark the point when transfer business truly gets going.
"We're still on holiday, we start next Monday. It's been a mixed break, with a lot of work and obviously a lot of thoughts about next season. After reaching the Champions League we want to still be protagonists, but for now it's still just talk," he said.
Asked whether he was in more regular contact with sporting director Tony D'Amico than anyone else these days, Gasperini explained the World Cup had slowed things down club-wide.
"We definitely speak a lot, but there's also constant dialogue with the ownership. Now that we're getting closer to the start of the season, to the transfer window... the World Cup shifted everyone's attention away from everything, for the players and for the agents themselves. From next week I think things will really get going."
On the club's three key contract renewals, Gasperini suggested announcements were close.
"For Dybala, Pellegrini and Celik, only the announcements are missing. The club will rightly handle that, we're certainly happy, including the players, it's a matter of days."
Asked whether incomings would prioritise wide players, he added: "Roma have shown they have a good base, a very solid and competitive group. The aim is to improve the squad as much as possible, and we'll try to work on every front - D'Amico in particular is extremely busy on all fronts - to keep giving satisfaction to Roma and our fans."
Reflecting on the season just gone, Gasperini acknowledged there had been a difficult spell.
"After the defeat to Inter things got tough, but this team, across 38 matches, only really struggled in two games when it came to the Champions League race. In a league like this there can be difficult moments, but we started well and had a great first half of the season. There was a tough spell between February and March, but as soon as we got everyone back fit we had an extraordinary end to the campaign, which allowed us to get back into the Champions League."
While those three contract situations move towards resolution, Soule's future looks less settled. The Argentine winger, who had already turned down lucrative offers from Saudi Arabia, is reportedly giving serious consideration to a move to the Premier League, with Sunderland having made an exploratory approach.
The English club's transfer business is overseen by sporting director Florent Ghisolfi, the same executive who knows Soule well, having signed him for AS Roma from Juventus in the summer of 2024. That relationship could prove significant should negotiations move forward, with Roma understood to be holding out for a fee in excess of €35million.
Borussia Dortmund remain another club Soule would be open to joining, but the German side have yet to make any concrete contact with Roma to open negotiations, a situation that, for now, leaves Sunderland with the clearer path should they decide to press ahead with a firm move for the Argentine.