The Colombia international was wanted by both clubs this summer but insists he is happy to stay with Fiorentina until the end of the season
It was reported in August that United were confident of signing the Colombia international this summer in a deal worth up to €37.5 million.
Barcelona now have a transfer ban in place which prevents them from making new signings until 2016, therefore United could reignite their interest without having to compete with the Spanish club for his signature.
"We had spoken with them [Manchester United and Barcelona] but the truth is that I’ve always remained calm," Cuadrado told reporters.
"I'm happy to stay another season, I'm fine here."