Cathro is the favourite to succeed Neilson should the 36-year-old complete his move to MK Dons.
Neilson confirmed after his team's victory over Rangers on Wednesday night that discussions were taking place after the Sky Bet League One club made an official approach on Monday.
While both clubs discussed compensation, Newcastle manager Rafa Benitez revealed he was in the dark over reports that Hearts had made his assistant coach, Cathro, their number-one choice to replace Neilson
Benitez said: "Ian is a great coach
We don't have any official approach
We are happy with him and we will continue with that
He is a young coach, he has some experience and has a great future.
"The media is telling me Hearts will come, but it depends on the head coach they have at the moment if he goes or not
That is football
It is just speculation."
Neilson was at Hearts' Riccarton training ground until late on Thursday afternoon.
The former Hearts full-back slipped out of Riccarton away from waiting media with the help of a masked decoy.
A member of the Hearts coaching staff, believed to be head of sports science John Hill, wore a Neilson face mask along with the outgoing head coach's initialled coat as he got into his car and drove off in front of the cameras.
Neilson is expected to be confirmed as MK Dons manager before their Emirates FA Cup tie against Charlton on Saturday.
Source : PA