Spanish media outlet Diario Gol say the Argentine superstar thinks Oyarzabal could be a more cost-effective option.
Barca made repeated bids to sign Brazilian ace Coutinho in the summer.
But Liverpool held firm and refused to sell their prized asset.
Oyarzabal is regarded as one of La Liga’s hottest prospects.
However, the elite are now circling.
Diario Gol say Messi isn’t the 20-year-old’s only admirer.
Real Madrid are also weighing up a swoop for the once-capped Spain international.
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Philippe Coutinho's dream five-a-side team
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“Liverpool star Philippe Coutinho is wanted by Barcelona”
Despite his relative youth, Oyarzabal has already racked up 69 appearances for Sociedad.
The versatile winger has 11 goals to his name having made his debut in 2015.
Barca could still swoop for Coutinho though.
Speaking earlier this week, the former Inter Milan man was coy when asked about Barca’s interest.
"I do not know how the future is going to be,” Coutinho said, leaving the door open to a fresh approach.
“What will happen in January, we will know it in January. I do not know if there will be an offer.”