"The president is offering voluntary repatriation to any Haitian that wants to return to their origin," said Mr Wade's spokesman, Mamadou Bemba Ndiaye.
Tuesday's earthquake killed tens of thousands and left many more homeless. Buildings have been reduced to rubble, the distribution of aid is slow, and people have been flooding out of the devastated capital, Port-au-Prince.
"Senegal is ready to offer them parcels of land - even an entire region. It all depends on how many Haitians come," Mr Bemba Ndiaye said.
"If it's just a few individuals, then we will likely offer them housing or small pieces of land. If they come en masse we are ready to give them a region."
The spokesman emphasised that if a region was given, it would be in a fertile part of the country rather than in its parched deserts, the Associated Press news agency reported.