Defoe left Spurs in January 2014 to sign for MLS side Toronto FC, but the 32-year-old has been linked with a return to English football.
The player himself fuelled the rumours on Tuesday, tweeting: “Just touched down in the UK from south of France, was training with my fitness guy feeling stronger than ever! #Ready”
QPR – managed by Harry Redknapp, who coached Defoe at Spurs and Portsmouth – and Leicester are among the clubs believed to be keen on a move for a player who has scored 124 Premier League goals.
He scored 143 goals for Spurs in all competitions during two spells at White Hart Lane.
Defoe, who will train with Tottenham’s development squad, has scored 11 goals in 19 games for Toronto, but his relationship with the club has deteriorated with injuries restricting his effectiveness.