Pacos de Ferreira, who finished third behind Porto and Benfica in the league last term, are keen to offer the United flop a route back to Portugal.
The 23-year-old is yet to start a Premier League game for the Old Trafford side since his multi-million pound switch three years ago.
He turned out for a United XI side on Tuesday against Barnsley - a game that also involved Nemanja Vidic and fellow want-away winger Nani. The match finished 2-2.
Bebe signed a five-year deal at Manchester United back in 2010, so he still has two years remaining.
He's already had two loan spells - one to Besiktas, another to Rio Ave - and he's made just two league appearances for United.
Sir Alex Ferguson admitted to never having watched the youngster live before he sanctioned the signing, and Bebe has become something of a punchline since he joined the club three summers ago.
He's unlikely to get much of a look in should he stay at Old Trafford, with Ashley Young, Nani, Antonio Valencia and Wilfried Zaha all ahead of him in the pecking order.
The fact he wasn't taken on the pre-season tour indicates that he's unlikely to play much of a role at Old Trafford next term.
Pacos de Ferreira recently found themselves in the press after one of their strikers, Rui Caetano, was put in a chokehold by Newcastle's Fabricio Coloccini during a match on the club's pre-season tour.