The 18-year-old has enjoyed a breakout campaign in LaLiga this season and is continuing to impress.
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Gunners boss Mikel Arteta is keen to bolster his defensive backline in the full-back position.
According to The Telegraph, the north London side have a 'serious interest' in the Real Valladolid right-back and have entered the race to sign him.
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The report does add, though, that Arteta could make a move for the teenage sensation at the end of the season.
Newcastle are also in the running for the youngster as they seek a replacement for Javier Manquillo.
Cedric Soares continues to be linked with a move away from the Emirates, with Fulham linked with the 31-year-old.
Ben White and Takehiro Tomiyasu are ahead of him in the pecking order, and with 18 months left on his current contract, and just 27 minutes of action so far, he could depart.
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Last week, Valladolid boss Pacheta, revealed Fresneda's time at the club could be coming to an end.
"I think Fresneda has few games left with the Real Valladolid shirt. He is 18 years old, but he does things that people of 30 do," he said.
"If I was at another club, I would go for him without hesitation, his data is brutal and you are not buying the current player, you are buying what he can become in a few years."
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Fresneda has made just 10 first-team appearances, but looks to be a future star.
Capped four times by Spain's Under-19 side, he was previously spent four years with Real Madrid as a youngster.
He currently has a release clause of £25million, which runs until 2025, and both Borussia Dortmund and Juventus have since joined the race for his signature.