The 24-year-old is currently a free agent after seeing his original deal with the Catalan giants expire at the end of last month.
However, one recent report claims that the France international has agreed to put pen to paper on a new two-year contract until June 2024, and Laporta has since revealed that an agreement is now in place.
The 60-year-old has also confirmed that they have reached an agreement with Leeds United to sign attacker Raphinha, which has since been announced by both clubs.
Speaking to reporters, via journalist Fabrizio Romano, Laporta said: "Yes, this week we'll sign and present Raphinha and Ousmane Dembele".
It is thought that an announcement on both deals is imminent, with head coach Xavi hoping to include both players in his squad for their pre-season tour of the USA.
Dembele, who has previously been linked with a number of top European clubs including Chelsea, Manchester United and Paris Saint-Germain, recorded two goals and 13 assists in 32 games for Barca across all tournaments last season.