Sanchez was back in Catalonia to begin his recovery after sustaining a serious knee injury in the win over Southampton earlier this month.
The 30-year-old was in Spain consulting knee specialist Dr Ramon Cugat.
Sanchez is facing eight weeks out with an injury that could end his season.
The forward spent three years at the Nou Camp scoring 39 goals in 88 appearances before his move to Arsenal in 2014.
Raul De Tomas on loan from Real Madrid fired Rayo into a 24th-minute lead, but Gerard Pique levelled for Barca before the break.
A Leo Messi penalty put the home side ahead, while Luis Suarez scored the killer third.
Barcelona are now seven points clear of Atletico Madrid.
Meanwhile, United, without Sanchez were beaten in the Premier League for the first time under Ole Gunnar Solskjaer at Arsenal.
Granit Xhaka opened the scoring and Pierre-Emerick Aubameyang sealed the win from the penalty spot.
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