Dembele has struggled with injuries over the past season and a half which has prompted the north London club to look across the channel for solutions.
Mauricio Pochettino is a long-time admirer of Geoffrey Kondogbia, 24, but the French international is on a season-long loan with Valencia, who have the option to make the deal permanent.
While Dembele was on the sidelines, Eric Dier, 23 and Harry Winks, 21, both emerged as a partnership for club and country, leaving the Belgian struggling to force his way back into the starting line-up since returning to full fitness.
With injuries a constant theme of the last two seasons, the Lilywhites are looking to the future and will listen to offers for their once-influential midfielder.
The list of replacements is being whittled down as well. 18-year-old Mateo Guendouzi of Lorient is another name bandied around the Tottenham hierarchy as a potential replacement. The French youngster has been capped by his country at Under-18, Under-19 and Under-20 levels.
Ajax’s Frenkie De Jong, 20, and Yves Bissouma, 21, of Lille are two other players who have caught Pochettino’s eye.