It appears likely Antonio Conte will end his short tenure at Spurs at the end of the season, when his contract expires. Conte will have spent less than two years at the helm of the north London side, leading them into the Champions League but proving unable to deliver a trophy.
Nottingham Forest's Steve Cooper and Brighton and Hove Albion boss Roberto De Zerbi have also played down links to Tottenham.
Amorim has attracted attention as one of Europe's brightest young coaches, impressing at Braga before joining Sporting in March 2020 and winning a Primeira Liga title in his first full season in charge.
Sporting were runners-up to Porto last season and are only fourth this term, but 38-year-old Amorim remains widely admired.