Enrique is currently taking a year's sabbatical from football following a three-year spell in charge of Barcelona, during which time he led the club to nine trophies.
However, Spanish publication Mundo Deportivo reports that he is keen to return to management next season, and would prefer to do so in the Premier League.
Champions Chelsea have been heavily linked with a move for the 47-year-old as speculation over Antonio Conte's future continues to grow after they slipped out of the top four in the Premier League table.
However, Chelsea could face competition from London rivals Arsenal, who have identified Enrique as a possible replacement for Arsene Wenger should the long-serving Frenchman step down from his role at the end of the season.
The Gunners currently sit in sixth place and could end the weekend eight points adrift of the Champions League places following their North London derby defeat to Tottenham Hotspur - the team's eighth loss of the campaign.
However, a number of other clubs are also thought to be interested in appointing Enrique, with Ligue 1 leaders Paris Saint-Germain, Italian giants AC Milan and even Serie A champions Juventus having been linked with the Spaniard.