Guillem Balague says that Barcelona have agreed deals to sign two free agents when their contracts are up in June.
Cesar Azpilicueta is in talks with the Spanish club over a free transfer.
Joan Laporta confirmed that the club had signed two players, but wouldn't name them.
He said that they had completed two signings for the next season.
Speaking to Catalan radio station Rac1, Laporta added: "One is a midfielder, the other one is a centre-back. But I'm not allowed to mention their names."
Kessie has played 215 times for AC Milan since moving from Atalanta in 2017, but he did not want to sign a new deal with the Italian club.
Since joining from Brondby as a 16-year-old, he has made 156 appearances for the club.
Azpilicueta is out of contract at the end of the season.
The sanctions placed on Roman Abramovich by Russia have made it difficult for him to offer new deals to his players.
The three players have been able to discuss terms with foreign-based clubs since they moved into the final six months of their contracts in January.
The Yorkshire club have asked to delay talks over a fee until next month so they can focus on their battle against the drop, according to the European football expert.
France forward Ousmane Dembele is likely to leave Paris Saint-Germain if Raphinha moves to the Barcelona Camp.
The club want to make Adama Traore's loan from Wolves permanent and will likely use Trincao as part of a swap deal.
Barcelona are not in the running for Erling Braut Haaland, who is expected to leave the club this summer.
Barcelona considered a deal for Haaland but could not match the numbers put on the table by Real Madrid and Manchester City.