Zidane surprisingly left his role as Real head coach last week and Pochettino was said to be President Florentino Perez' number one target to build on the unprecedented success of the Frenchmen.
However, after it was revealed that Pochettino no longer holds a release clause in his most recent five-year contract he signed with Spurs, the 13-time European champions have since abandoned their attempts to lure him back to Spain.
According to Spanish football expert Guillem Balague, Perez has come to terms that the negotiations with Daniel Levy is not worth the hassle, given their protracted tranfer saga's with Garteh Bale and Luka Modric in the past.
"Real could see there was so many positives in signing him, not just the fact he can deal with the stars but how he improves players and how he works with youth players as well.
"But what they had in front of them was the possibility of negotiating with Daniel Levy for perhaps a month, even longer, with no guarantees whatsoever that they were going to get him.
"That makes life very difficult for Real Madrid. They will have to look at other possibilities including all the managers that are already in a job with a contract," he added.
"Real started fishing and put the idea out there in the media to see what the reaction was, but straight away they realised there was no clause for Pochettino to leave."