As the Mirror report, Palacios had to withdraw from Argentina's Copa America squad due to a hamstring injury.
But when asked about his future, the 20-year-old revealed that he was aware of interest from Europe:
"I’m proud clubs like Real Madrid and Arsenal are interested in me," he said.
Palacios played a key role in River Plate's historic Copa Libertadores win against Boca Juniors late last year.
He was rumoured to be on his way to Madrid for £20 million in 2018, but the interest cooled after he suffered a ligament injury.
Palacios's release clause now stands at £18m, which is affordable for Arsenal amid their tight financial constraints this summer.
With Mesut Ozil reportedly on the transfer market plus Aaron Ramsey, Stephan Lichtsteiner and Danny Welbeck leaving on free transfers, there could be some increased activity with incoming players this summer.
Arsenal are also rumoured to be closing in on Brazilian youngster Gabriel Martinelli, and have registered interest in Boca Juniors' Nahitan Nandez and Emanuel Reynoso.
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