The Spain international's move to Chelsea is expected to result in the Blues allowing their current number one Thibaut Courtois to join Real Madrid in a £35 million deal. However, the Spurs will need to hurry to complete a deal as the English transfer window will be closing it's doors on Thursday.
Last month, Italy worldwide striker Eder made such a move, swapping the Serie A club for Suning after two and a half seasons in Milan.
Kovacic has been agitating for a transfer in the close season and told the Spanish daily in June that it was owing to his lack of first-team chances.
On Monday, Kovacic reportedly chose to train alone at "Ciudad Deportiva" in order to decide on his future and potentially force an exit.
They already have three Croatian players - Marcelo Brozovic, Ivan Perisic and new loan signing Sime Vrsaljko from Atletico Madrid.
But Julen Lopetegui was firm in saying that Modric is staying with Real Madrid and going nowhere this summer. Kovacic is linked with the return to his former club Dinamo Zagreb from where he started his playing career.
Kovacic, 24, moved to Real from Inter Milan in the summer of 2014.
He said of the Chelsea target: "You speak to me about problems with Kovacic, but I know nothing about any of this".