Sigurdsson spent two years at White Hart Lane between 2012 and 2014 before returning to Swansea City in search of regular first-team football.
England striker Kane was attempting to force his way into the first-team picture at Spurs during that time and was seemingly keen to display his goalscoring prowess on the training pitch.
Sigurdsson, who will face Kane for the first time since helping Iceland knock England out of Euro 2016 when Swansea visit Spurs in the Premier League on Saturday, was not always impressed with Kane’s single-minded approach to scoring goals in training.
However, he expects the 23-year-old - who signed a new contract at Tottenham until 2022 on Thursday - to be the main man at Spurs for the forseeable future.
“You can tell in training that he wanted score goals,” he told Omnisport.
“It was a little bit annoying sometimes and I think I had a chat with him.
“With young players you never know how quickly they’re going adapt.
“But he’s been outstanding for the club and I think he’ll be their main man in the next few years. Even now he is their main man.”