The French midfielder has been linked with a move to the club since Juande Ramos replaced Bernd Schuster as Real Madrid coach.
“We have always said that we would only allow our players to leave if we received an exceptional bid,” a Portsmouth spokesman told the club’s official website.
“We could not stand in the way of a move such as this for Lassana.
“It shows how far the club has come under the ownership of Alexandre Gaydamak when Real Madrid come in for one of our players.
“Should the deal be completed, the club has already identified possible replacements.”