The 20-year-old only arrived in the French capital last year but looked set for a move to Barcelona following PSG’s capture of compatriot David Luiz.
The Spanish club were reported to have already have agreed a deal in principle for the former Corinthians man, but Blanc insists he is staying put.
“He will certainly stay,” Blanc told RMC.
“I'm interested in keeping the same group we had this year.”
Brazil international Dani Alves was rumoured to be a makeweight in the deal that will take the defender to Camp Nou, and Blanc refused to rule out a separate move for the right-back.
“Dani Alves is one of the top players at his position,” said Blanc.
“We have already acquired David Luiz and at least one or two more players will arrive this summer.”
Marquinhos made his international debut as a substitute in Brazil's 5-0 victory over Honduras in November but failed to earn a place in Luiz Felipe Scolari's World Cup squad.