Spurs opened talks with Real about the 23-year-old, a Croatia international, weeks ago with a view to a £22m swoop.
But he now looks set to join Juve, with the player’s representatives expected to meet with the Italian giants in the next few days.
Real are ready to let Kovacic leave but Spurs have yet to follow up their interest with a firm bid and now face losing out.
Mauricio Pochettino has so far endured a frustrating summer with no incomings and Kyle Walker sold to Manchester City.
An ankle injury to Kieran Trippier, who will miss the start of the season, has now left Spurs short at right-back and looking for cover.
The north Londoners were in the running for Paris St-Germain misfit Serge Aurier earlier this summer.
But no progress has been made there either, with Chelsea now joining Manchester United in the race to sign him.
Spurs have also abandoned their interest in Porto’s Ricardo Pereira, who can play in either full-back role.
But they remain interested in Valencia right-back Joao Cancelo, who is valued at £25m by the Spanish side.
Left-back Danny Rose, who will also miss the start of the season with a knee injury, has also been told he is going nowhere.
United and Inter Milan remain interested in the 27-year-old England defender but Tottenham have no intention of letting him leave.
Spurs are also weighing up a loan offer from Trabzonspor for Moussa Sissoko. They would prefer a permanent transfer.
