Kane included in Spurs' pre-season squad as Lloris left out
England captain Kane is in the final 12 months of his contract with at north London side Spurs but is said to have attracted interest from German giants Bayern Munich amid reports their initial 70-million-euro (£60m) bid for the forward was rejected by the Tottenham hierarchy.
Kane, along with other international players, returned for pre-season training on Wednesday, when new Spurs boss Ange Postecoglou was set to outline his vision to the club's leading scorer.
Spurs said Friday that veteran goalkeeper Lloris had been granted permission not to travel "in order to explore prospective transfer opportunities".
At the age of 36, the former France No 1 has been linked with a move to Inter Milan should Andre Onana join Manchester United.
Lloris, who joined Tottenham in 2012, has made 447 appearances for the club and also won the 2018 World Cup with France.
Tottenham will fly to Perth, Western Australia, with their squad including new signing James Maddison following the England midfielder's £40 million move from Leicester, ahead of an opening friendly against top-flight London rivals West Ham on July 18.
Spurs play Leicester in Thailand on July 23 and the Lion City Sailors of Singapore on July 26.