Kane will have a year left on his contract at Tottenham in the summer and has been heavily linked with a move away from the north London club.
Manchester United are interested in taking the 29-year-old to Old Trafford, but are wary of getting into negotiations with Daniel Levy.
Bayern Munich are another potential destination for Kane, with the Germans firm admirers of his talents.
Tottenham are expected to bring in a new manager in the summer and it is suggested their interest in Enrique is partly driven by their goal to hold onto the talismanic forward.
The Spaniard is the favoured option for Fabio Paratici, who wants to bring the former Barcelona boss to north London.
Tottenham also believe getting a manager of his stature would convince Kane to commit his future to the club.
Enrique has been out of work since leaving Spain after the World Cup and is open to holding talks with Tottenham.
Mauricio Pochettino has also been linked with a move back to Spurs, but the club hierarchy are split on reappointing the Argentinian.
