The Belgian international, 26, has impressed at Goodison Park since his £6m switch from Olympiacos in 2012, and is expected to feature for his country at the World Cup in Brazil this summer.
But they could be forced into a decision over his future, with speculation linking Premier League rivals Spurs with a £12m bid for the former Lille man - which would be twice as much as they paid for him just two years ago.
After an impressive season under Roberto Martinez, Everton can expect to receive plenty of interest in some of their star players, but had anticipated moves for Ross Barkley, Leighton Baines or Seamus Coleman rather than Mirallas, who is being eyed up to join the Belgian contingent at White Hart Lane.
Fellow internationals Jan Vertonghen, Moussa Dembele and Nacer Chadli all currently play their football for Spurs, and this could be an important factor should Mirallas push for a move away from Merseyside.
But the speculation is somewhat perplexing given that there are still huge question marks over the managerial position in North London. Tim Sherwood replaced Andre Villas-Boas in the hot seat back in December, and despite earning some impressive results since taking charge, it's believed that chairman Daniel Levy is looking to bring in more of an experienced head in the summer, with Cesare Prandelli of Italy and Holland's Louis van Gaal linked with post-World Cup switches.
Everton's long-term goal under Martinez will be to break into the top four, and they would hate to weaken themselves and strengthen a rival in the process, but £12m for Mirallas - who has scored 14 goals in 63 games for the Toffees - could be too good to turn down, whilst Martinez has recently strengthened his flanks with the signing of Aiden McGeady, which could make Mirallas available at the right price.
image: © Erik Drost