The Evening Standard understands Kane is very confident he will be included in the squad as Spurs bid to win the Champions League for the first time on June 1.
Kane has not played since suffering a ligament injury to his left ankle against Manchester City in the quarter-final first leg back in April, with Spurs fearing his season was all but over.
However, the England striker – who is also expected to feature for the Three Lions in the Nations League finals – has made a quicker than anticipated recovery.
The 25-year-old, who has scored 24 goals for Spurs this term, has stepped up his rehabilitation in recent weeks.
Barring any late setbacks, Kane will be on the plane to Spain to face Jurgen Klopp’s men.