The Whites are looking to add to a squad which head coach Uwe Rosler has claimed to be on the small side, with the German insisting that despite a summer of busy recruitment he only has 18 first team squad members.
Veljkovic is of interest to the Whites, however according to the Yorkshire Evening Post, Leeds have so far refused to provide any assurances over the amount of football he could expect to play at Elland Road.
With the move for the 19-year-old Serbia Under-21 international likely to take the form of a loan switch, Spurs are reluctant to send him to Leeds without guarantees over playing time.
The Swiss-born Serbian has been out on two loan spells to Championships clubs already with Middlesbrough and Charlton Athletic.
Spurs signed Veljkovic from Swiss giants FC Basel in 2011, drafting him into their youth ranks.
He has won the European Under-19 Championship and the FIFA Under-20 World Cup with Serbia, in 2013 and 2015 respectively.