Tottenham have had their eye on the 20-year-old for some time and now and aim to complete the deal before their second game of the Premier League season against Chelsea.
The Spain youth international would become the North London side's first signing of the current transfer window.
Spurs have failed with several of their transfer targets this summer, including Everton midfielder Ross Barkley. The Toffees asking price of £50m is proving to be a major stumbling block in negotiations for the player.
They have now turned their attention to Diop, who made 19 appearances for Celta Vigo last season, only five of which were starts in La Liga.