Kane suffered a serious set-back on New Year's Day, when he limped off the field during Spurs' 1-0 defeat against Southampton.
He played no role in his side's next clash, a 1-1 FA Cup third round draw away to Middlesbrough, as subsequent tests revealed that the forward had sustained a ruptured tendon in his left hamstring, promising a lengthy lay-off.
On Thursday, Tottenham confirmed that Kane will need surgery and will miss at least three months of action, all but ruling him out for the rest of the Premier League season.
Spurs have been left short of options up front, with few players in the current squad seen as natural centre-forwards.
Lucas Moura and Son-Heung Min partnered each other in attack against Middlesbrough, but could only muster one goal against Championship opposition as they were held to a disappointing draw.
And while Edinson Cavani has been mooted as one ambitious possibility to fill the void left by Kane, sources close to the situation have confirmed to Goal that Dembele is on Spurs' radar.
The striker has been one of the few positives in what has been a poor season overall so far for Lyon, who languish in 12th in Ligue 1, seven points behind Rennes and the third and final Champions League qualifying spot.
Dembele leads the scoring charts for his side with 10 league strikes, just three shy of Ligue 1 top scorer Wissam Ben Yedder at the halfway stage.
He was on target again this week, netting twice in Lyon's 7-0 Coupe de France thrashing of Bourg-Peronnas before adding another in the Coupe de Ligue on Wednesday to send his side through to the semi-finals at the expense of Brest.
That prowess in front of goal has caught Spurs' attention, and they see Dembele as an able deputy for the rest of the season while Kane recovers from his operation.
No formal bid has been filed for his services, however, and Lyon have already made clear that they are not interested in a January sale amid reported links with Chelsea.
"L'Olympique Lyonnais are aware of certain reports in the media which suggest that Moussa Dembele could be of interest to other clubs during this transfer period," the club explained in a statement released January 2.
"L'OL would like to reaffirm their wish, just as in the 2019 summer window, to keep Moussa Dembele. The club has total confidence in Moussa and counts on him to form part of a competitive team for seasons to come."