Burdisso, who plays for Argentine outfit Rosario Central, has apparently courted interest from the Premier League pair.
The defender is highly-rated and has attracted interest from a host of Italian teams previously.
Guillermo's older brother Nicolas currently plays for Serie A outfit Roma but it appears a move to England looks likely for the 22-year-old.
Burdisso - who has a solitary Argentina cap to his name - says he is waiting for news as to which half of the North West city was looking to snap him up in the close season.
He said: "I have been told that in the next days an offer from Manchester is going to arrive to the club and that when that happens the manager, Vicente Cunado, is going to tell me if it's from Manchester City or Manchester United.
"In addition, according to what is being said by the press of Rosario, it seems to be that what has been offered is what Rosario Central expects my transfer."