Varela is highly-rated by assistant boss Ryan Giggs and could be offered an improved deal by United.
However the chance to go and play regularly in Italy for a few months appealed to him as he told El Pais: “At my age it’s so important to play more minutes.
“But I’m also aware that its important and a good thing if your coach wants you to stay and counts on me.”
United currently have Ashley Young, Luke Shaw, Marcos Rojo and Antonio Valencia all sidelined with injury.