A tweet from one of United's sponsors stated a loan deal was in place, however there has been no official confirmation from either club.
New Bluebirds boss Solskjaer has already brought in former United youngsters Magnus Wolff Eikrem and Mats Moller Daehli, and is believed to be keen on short-term moves for Fabio and winger Wilfried Zaha.
Press Association Sport understands talks over a deal for Brazilian Fabio to move to south Wales until the end of the season are ongoing, and Cardiff are hopeful the 23-year-old, who spent last season on loan at QPR, will make the switch.
The verified Twitter account of Airtel, United's telecommunications partner on the sub-continent, stated that Fabio could not take part in a planned question and answer session with twin brother Rafael on the social media site, because a move to south Wales had been agreed.
The tweet on the @airtelindia feed, which was later deleted, read: "Unfortunately, Fabio will be joining Cardiff City on loan till the end of season & hence only Rafael will join us for #airtelAskUnited".