Interior Minister Bernard Cazeneuve is to announce the move on 30 May during a visit to the camp during which he will be accompanied by Housing Minister Emmanuelle Cosse, the paper says.
The decision is "very good news", MSF's André Jincq told Le Monde.
Grande Synthe Mayor Damien Carême, a member of the Green party EELV, also welcomed it.
Carême was promised state help when he met Cazeneuve last September after the number of migrants in his town grew from a few dozen to 2,500.
But the aid was not forthcoming and the local council itself built showers and garbage disposal facilities and went on to plan a camp with wood cabins with MSF.
Despite differences with regional and national authorities the camp opened on 7 March and, according to Le Monde, Cazeneuve promised that the government would help with financing the camp's infrastructure on 31 March.