Spurs chairman Daniel Levy is said to have held talks with the striker and his representatives, and is hopeful of securing a deal quickly.
The Sun's report claims from their sources that N'Jie is keen on a move to the North London club, with seemingly the only stumbling block being whether the two clubs can agree a fee.
Lyon and their president
Lyon president Jean Michel Aulas is comparable to Daniel Levy for his ability as a tough and seasoned negotiator in the transfer market.
Spurs last struck a deal with Lyon for goalkeeper Hugo Lloris back in 2012, but it remains to be seen how prepared the Ligue 1 side are to dig in if they want to hold onto a player who has a contract at the club until 2019.
N'Jie vs Martial
If Tottenham move for N'Jie, it could end their interest in Monaco attacker Anthony Martial, previously reported by France Football.
N'Jie is two years older at 21, but both play in similar positions, able to impress both up front and out wide.
While Martial has been likened to former French international Thierry Henry, N'Jie has to deal with inevitable comparisons to Samuel Eto'o, as a Cameroon international, with nine caps and four goals to his name.
N'Jie scored eight goals and provided nine assists in all competitions last season, with Martial scoring 12 and creating five.