Neilson will take charge of the game against the Ibrox men this evening, and will be unveiled as MK Dons new gaffer tomorrow.
Cathro’s appointment could be confirmed this week, although it may be that a caretaker boss will take charge of Saturday’s game against Ross County.
He also looks likely to have scope to appoint a new assistant, with current No2 Stevie Crawford set to follow Neilson across the border.
Craig Levein, the Hearts Director of Football, is a fan of Cathro and made him head of Dundee United’s academy in 2008 when he was just 22. He then moved onto the SFA Performance schools programme.
In 2014, he made a surprise switch to Portugal to become assistant boss at Rio Ave before moving to Valencia to link up with Nuno Espirito Santo, with whom he had worked in Portugal.
Cathro was taken to Newcastle by ex-boss Steven McClaren in June 2015 and stayed on when Benitez took charge last season.