Conte is under pressure after losing back-to-back Premier League matches against Bournemouth and Watford.
Chelsea are believed to have drawn up a list of potential replacements, with Enrique top on the list.
The Telegraph UK, reports that the 47-year-old is busily ‘preparing’ himself for a move to England.
Reports in Spain have also suggested that the former Roma manager has also drawn up a list of transfer targets and has made Luis Suarez his first priority.
He would relish the challenge of going up against old teammate Pep Guardiola, as well as Jose Mourinho.