The north London club want to bring in a left-footed centre-back as part of Antonio Conte’s plans to strengthen the squad.
Alessandro Bastoni has been the priority target but his agent recently claimed that the defender will not be leaving Inter, seemingly ending Tottenham’s chances.
Spurs are also considering a move for Josko Gvardiol, but RB Leipzig are believed to want around €80m before agreeing to sell him this summer.
19-year-old Zabarnyi has been identified as an alternative target but it has been claimed that even he would not come cheap.
Dynamo Kyiv are aware of the level of interest the teenage centre-back has been attracting and want an appropriate fee.
The Ukrainian outfit want around €30m before they would consider selling the centre-back this summer.
The 19-year-old has already made 59 senior appearances for the club and has 20 international caps to his name for Ukraine.