Press Association Sport understands the bid was submitted Monday evening Sydney time and thus far there has been no response.
If the deal did go through it would represent David Moyes' first significant signing as United manager.
United were heavily linked with the former Arsenal skipper earlier in the summer, although at the time Fabregas claimed his intention was to remain with Barcelona.
Moyes then turned his attentions to Fabregas' Barca team-mate Thiago Alcantara.
At one point it seemed as though a deal for the Spain Under-21 star was nearing completion.
However, at the 11th hour Pep Guardiola stepped in and Thiago has now agreed to join Bayern Munich.