Gallardo has been tipped to succeed Ernesto Valverde in the Camp Nou hotseat after a mixed start to the 2018/19 campaign.
The Spanish champions currently sit on top of the La Liga table, but only on goal difference ahead of Real Madrid and Real Sociedad, while Atletico Madrid and Sevilla are just a point behind.
Pressure has increased on Valverde after his side fell to a 3-1 defeat to Levante last weekend, before being held to a 0-0 Champions League draw by Slavia Prague in midweek at home.
When asked about the possibility of Gallardo leaving Buenos Aires for Catalonia, River Plate sporting director Enzo Francescoli refused to shoot down the speculation.
"We need to be prepared for any decision," he told TYC Sports.
"This happened a few years ago when Ramon Diaz told us he had to leave, but I don't think about this a lot.
"You [the media] make me think about this when I speak with you.
"I'm not thinking about what'll happen in a couple of months because it's not even my decision.”
Meanwhile, World Cup-winning former Argentina international Claudio Borghi was much more confident that the change will take place.
“Gallardo will be coach of Barcelona in December," he said.
"He is one of the best coaches in the world.
"[River Plate president Rodolfo] D'Onofrio said he'd only leave by quitting his post, but I know this from a direct source."
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