The young Brazilian left-back is set to leave Old Trafford to gain more regular first-team football as he continues his development
The 21-year-old has made only one Premier League appearance this year, mainly featuring in the United reserve team.
"He understands the value of playing regularly at a higher level than we can give him at the moment," Sir Alex told United Review.
"I hope that Fabio will develop the same way as his twin [Rafael]."
Opportunities for the young left-back have been further restricted by the form of Patrice Evra and several injuries.
His 14 appearances have come mainly in the League Cup and Champions League this season.
The Da Silva twins moved to Manchester from Fluminense (without having played in the Brazilian club's first-team) in January 2008, but were unable to play in matches until they turned 18 in July 2008.
Rafael's first start for United came on 23 September that year, while Fabio's competitive debut was delayed by a shoulder injury that required surgery. He finally broke into the first-team 24 January 2009, in a 2–1 FA Cup fourth round win over Tottenham.