The Middle House, at Mayfield, has confirmed he has paid two visits there recently but would not offer further details.
Pirates of the Caribbean actor Depp, 55, is rumoured to be considering buying television presenter Davina McCall’s £3.2 mansion in nearby Wadhurst.
He was reported to have enjoyed a Sunday lunch at The Middle House, along with his manager and two other people, dressed in a cowboy hat and scarf on his second visit to Mayfield.
The picturesque timbered pub, which dates back to 1575, is no stranger to celebrities, with former Big Brother presenter McCall, actress Cate Blanchett and rock guitarist Jeff Beck all there on a single day recently, according to a regular.
Depp, who rose to international stardom in the film Edward Scissorhands, last year divorced wife Amber Heard in a highly public and acrimonious split.
The six-bedroom house he is reportedly showing an interest in comes complete with 38 acres of private parkland, its own swimming pool and tennis court.