Gunners boss Mikel Arteta is a massive admirer of right-back Fresneda, a product of Real Madrid's youth academy, and is hoping to push through a deal this month.
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Wolves have also shown an interest in Fresneda but were eying him for a move next summer.
The 18-year-old has broken in Vallodolid's first team this season, and shone from right-back in LaLiga.
So much so that Spanish outlet Marca report he will almost certainly become the biggest sale in Valladolid's history, with numerous European sides waiting to make offers.
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Speaking earlier this month, Fresneda said: "It's nice to be linked to big teams in Europe, but I belong to a historic club in Spain like Real Valladolid.
"I am focused on the team and outside of possible negotiations, that takes my representative. My wish today is to play here.
"What it's more to come every day and sit next to players with the career of Roque Mesa, Sergi Guardiola or Sergio Leon, or play against Vinícius, for example, whom I recently watched on television.
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"I still live in the Club's Players' Residence and I watch a lot of football. I started studying Sports Management after taking the university entrance exams."
Premier League leaders Arsenal have already strengthened this month with £27million signing of Leandro Trossard from Brighton.
They appear set to follow that up with a £22m deal for Spezia defender Jakub Kiwior, with Fresneda next among their targets.