Both clubs held talks over a deal to sign Coric in the summer but the 19-year-old playmaker decided to stay in Zagreb and review his options in January.
Coric pulled out of a proposed £15m move to Manchester City in August after learning that Pep Guardiola planned to send him out on a season-long loan.
City are unlikely to make a renewed bid for Coric, but the midfielder is expected to leave Dinamo in January and would prefer a move to the Premier League despite interest from leading clubs across Europe.
The Reds have been tracking Coric for more than two years and have been in regular contact with his representatives over a potential deal for one of the most highly rated youngsters in European football.
Spurs hope to take advantage of their good relationship with Dinamo dating back to Luka Modric’s move to White Hart Lane in 2008 and believe Coric fits their philosophy of signing talented young players with potential to improve under Mauricio Pochettino.
Everton have also made enquiries over the midfielder and hope to tempt Coric with the promise of more regular playing time than he could expect at Spurs or Liverpool.
Dinamo Zagreb are said to have been disappointed when Coric’s proposed transfer to City fell through and will demand at least £15m to sell their star player in the new year.
The club have made the decision to sell Coric, with the team almost certain to be out of European competition at the end of the Champions League group stage, where they sit bottom of their group having lost all four of their matches so far.
Coric has been compared to Modric for his sleight frame and technical ability, but prefers to play in a more advanced role than his compatriot, operating in a central No.10 role or from the left flank.
Coric has already played 102 matches for Dinamo Zagreb, scoring 15 goals and providing 19 assists for the side.