'The Sun' reports that the former Barcelona boss heads both sides' wishlist as they look to for successors for Arsene Wenger and Antonio Conte respectively.
Wenger announced on Friday that he would leave the 'Gunners' at the end of the season, ending his remarkable 22-year tenure, whilst Conte is also expected to move on as a result of the friction between himself and the board over transfers and Chelsea's rather limp attempts to defend their title.
The aforementioned source claims that Arsenal have opened talks with the Spaniard, despite Chelsea having already been at an advaced stage of negotiations with the 47-year-old.
The 'Blues' are thought to be reluctant to allow Enrique to bring in a horde of backroom staff, with the former Spanish international having worked with five coahces, four physios and a psychologist during his time at Barca.
Both Brendan Rodgers and Patrick Vieira have distanced themselves from the Arsenal post in recent days, making Enrique's name all the more intriguing in the corridoors at the Emirates.