Deschamps: We can only do loan deals
OM will lose several key performers to the CAF Africa Cup of Nations later this month but Deschamps said they cannot afford to buy new players to replace them.
"Lots of players would like to come here or hope to come here," said Deschamps.
"We've been offered tens of them. We could have had four or five in training today. But we can't invest, so it will have to be in the shape of a loan.
"It'll obviously be a player who isn't playing at his current club. The equation isn't easy to solve."
Marseille face third-tier Red Star in the French Cup on Saturday, after which Andre and Jordan Ayew (Ghana), Souleymane Diawara (Senegal) and Charles Kabore (Burkina Faso) will depart for the Africa Cup of Nations in Gabon and Equatorial Guinea.
Deschamps hopes to keep the Ayew brothers for the League Cup quarter-final at Caen on Tuesday but admitted it would be "complicated".
Despite speculation about the futures of striker Andre-Pierre Gignac and playmaker Lucho Gonzalez, Deschamps said the arrival of new players would not depend on OM's ability to sell members of the current playing staff.