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]."
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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.
To date Fabio has made 53 first-team appearances for United (21 of them in the Premier League), while Rafael has nearly 90 to his name (49 in the Premier League).