Spurs boss Mauricio Pochettino is said to be a long-time admirer of the U19 Spain international and submitted a bid of £10m for the midfielder 10 days ago.
However, Lyon are now close to signing the 20-year-old after bettering the offer submitted by the Premier League side.
The Ligue 1 outfit outbid Spurs with an offer of £13.8m plus £9m in add-ons and hope to confirm the signing over the next 24 hours
Pochettino was hoping to add Diop to his summer acquisitions after confirming the signings of Davinson Sanchez and Paulo Gazzaniga earlier this week.
But now Tottenham are considering other midfield and forward options ahead of the transfer deadline on Thursday.