Everton and Arsenal have both looked shaky at the back so far this season.
Both Arsenal and Everton are in need of a centre-back, with both sides struggling defensively throughout the campaign so far.
Nunez has a £30 million release clause and it is thought that he could appeal to both Unai Emery and Marco Silva, as they target January additions.
Whether Nunez would be interested in a move to the Premier League remains to be seen.
But the 22-year-old did suggest that he wanted more game time towards the back end of last term.
“I want to succeed at Athletic. It’s the team of my dreams, but I want to play as much as possible,” he said to Inside Athletic in July.
“I can’t say that Yeray and Iñigo don’t deserve to be starters.
“They’re incredible players but I think I can be at their level. It’s an uncomfortable and difficult situation. I will fight my best to win a starting role and convince the coach.”
Nunez has only played in three of Bilbao’s eight games so far this term, which is unlikely to have satisfied his cravings for first-team football.
The one-time Spanish international could be more likely to feature at both Arsenal or Everton.
Everton have only Michael Keane, Yerry Mina and Mason Holgate as recognised senior centre-backs, and none of the trio have looked entirely convincing.
Arsenal, meanwhile, have struggled defensively throughout the campaign, although the return of Rob Holding to fitness should help them tighten up at the back.
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