The 23-year old Brazilian full-back, who spent last season with QPR, has only been used a total of three times by David Moyes this campaign and could be sent to Cardiff this month.
New Bluebirds boss Ole Gunnar Solskjaer is keen to strengthen his defence and knows Fabio from his time as a youth coach at United before he took the reins at Molde.
A post on Twitter from one of United's sponsors, Airtel India, suggested that a deal was set to be completed before it was quickly taken down.
"Unfortunately, Fabio will be joining Cardiff City on loan till the end of season & hence only Rafael will join us for #airtelAskUnited," read the post during a proposed Q&A with Fabio and his twin brother Rafael.
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