The Toffees took on the Spanish side in a pre-season friendly earlier this week, which they lost 3-1.
All of Celta’s goals came in a 16-minute period, and were netted by the diminutive Spaniard.
This is rumoured to have seen the Merseysiders’ interest spike, with a move for the former Barcelona starlet a possibility.
But the La Liga minnows are ready to demand £8m in a bid to keep hold of the 27-year-old.
Nolito’s camp are aware of the glances from Everton, but there has been no official contact as of yet.
The player is under contract at the club until 2017 and netted 14 league goals last season.
Nolito spent some time at Barca earlier in his career after impressing for their B team following a journey through Spain’s lower leagues.
He failed to establish himself at the Camp Nou before heading to Benfica, whom he left in 2013 to join Celta after a brief loan spell at Granada.