Last week, Memphis indicated that he was aware of interest from Barca, but at that point negotiations were still in their infancy.
On Tuesday, talks developed to the point where a fee has now been agreed, according to De Telegraaf.
Ronald Koeman recently took over as Barcelona boss following the 2019/20 campaign which saw the Blaugrana fail to win a trophy for the first time in 12 years.
The Dutchman was selected to replace Quique Setien, with one of his main tasks in this summer to revitalise an ageing squad.
Ivan Rakitic has already been sold to Sevilla, while Luis Suarez and Arturo Vidal look set to depart for Juventus and Inter respectively.
Koeman's two main targets for the transfer window have been Gini Wijnaldum of Liverpool and Memphis, and although there have been no major developments with the latter, the former Barca player is set to land the Lyon captain.
For Barcelona, Memphis will crucially link up with Lionel Messi, who previously asked for his contract to be terminated this summer only to change his mind and confirm he is staying for at least another year.
Reports indicate that Memphis could take the number 9 jersey from Suarez.