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Enrique enjoyed a successful three years in charge at Barcelona before deciding to take a season out of football last summer.
The Spaniard has now reportedly decided to make return to the dugout for the 2018/19 campaign.
And according to Spanish outlet Mundo Deportivo, the Premier League will be Enrique’s next destination.
Chelsea boss Antonio Conte has come under increasing pressure in recent weeks despite leading the Blues to the Premier League title last season.
The Stamford Bridge outfit sit fifth in the table and 22 points behind league leaders Manchester City, and reports suggest Conte is in line to be sacked in the summer.
Chelsea are said to have already made an approach for Enrique, but that also promoted a move from Arsenal.
The Gunners hierarchy will decide at the end of the season whether to keep faith in Wenger, who has a year remaining on his contract.
But with the north London club looking likely to miss out on Champions League football for a second successive season, they may have no option but to replace the Frenchman.
Mundo Deportivo add that Chelsea are in pole position to land Enrique, who has also attracted interest from Paris Saint-Germain.