The La Liga champions are ready to launch a bid to stop the 21-year-old being snapped up by Real Madrid or AC Milan.
According to the Express, Barcelona are set to hijack a move for the England international in January.
Rashford's future at Old Trafford has been questioned following his shaky spell of form under Jose Mourinho.
He has scored just five goals and made five assists for the Reds this season.
And he could look to continue his career elsewhere if he does not improve during Ole Gunnar Solskjaer's reign in the hot seat.
The temporary United boss did name Rashford in his starting line-up for his first game in charge on Saturday.
And the striker showed the manager what he is capable of when he scored a free-kick after just three minutes during the 5-1 win.
His sublime strike even forced a smug smile out of Old Trafford vice-chairman Ed Woodward in the stands.
But the club will face a fight to keep hold of him after AC Milan also set their sights on him.
The Italian club failed to lure Zlatan Ibrahimovic back to the San Siro, so Rashford is now the top target.
Real Madrid have also indicated interest, but are not expected to spend big in the upcoming transfer window.
SunSport exclusively revealed last month that Rashford will talk to the La Liga side if he does not cement his spot in United's first-team.
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