The Gunners were thrown into turmoil on Wednesday after it was announced that a £24 million deal had been agreed with Manchester United for the transfer of captain Robin Van Persie.
Arsene Wenger has began searching for the Holland internationals successor and Mirallas was top of his shortlist but has been beaten to the punch by David Moyes.
The Toffees have money to burn after scooping £12m from the sale of Jack Rodwell to Manchester City and are prepared to invest around £5.3m in the 24-year-old frontman.
Moyes has been on the lookout for someone to partner Nikicia Jelavic at Goodison Park next season and has moved quickly to capture the Belgian stars signature.
Mirallas admits he favours a move to Merseyside where he will be guaranteed first team football unlike in North London where he would battle Oliver Giroud and Lukas Podolski for a starting spot.
“It is possible to go to Everton, it is possible to go to Arsenal, I don’t know now,” Mirallas told Sky Sports News.
“I will speak with my manager and make a good decision for me and also speak to my family importantly.
“They are two big clubs of the Premier League, but for me it is more important to play every week. It is better for me a little bit at Everton.
“They [Everton] are a good team and it is a good opportunity because Marouane Fellaini plays at Everton who is my friend, but I don’t know.
“Tomorrow I go to Greece, next week I go to the Premier League or go to Superleague Greece.”
FC Copenhagen’s left-back Bryan Oviedo is also on Moyes radar as he looks to bring cover in for England international Leighton Baines and could make his move once Mirallas has completed his switch.