The Portugal star, who won Euro 2016 earlier this summer, is believed to be of interest to Mauricio Pochettino at White Hart Lane.
Ahead of their venture into the Champions League, the North London outfit are said to be on the hunt for attacking reinforcements.
The 27-year old has established himself as a stalwart in the Portuguese capital since moving to the club as a youngster from Bordeaux.
With 46 caps at international level, the central midfielder is a seasoned veteran, though both Everton and AC Milan are understood to be on a move.
Christian Eriksen is also thought to be a target for the likes of Inter Milan and Juventus.