The Frenchman won three UEFA Champions League trophies in a row with Los Blancos, and Short said Perez wanted him to take "at least a year away" from top-level management following his departure from the Santiago Bernabeu.
Short called Zidane a "viable option" for United, as El Confidencial said Mourinho remains "on a tightrope" at Old Trafford.
The Sunday Mirror's John Richardson noted how Real pair Toni Kroos and James Rodriguez, Bayern Munich playmaker Thiago Alcantara and striker Edinson Cavani of Paris Saint-Germain would be on United's wishlist with Zidane as manager.
However, ESPN FC's Julien Laurens (h/t Lewis Winter of the Daily Express) doesn't believe Zidane has "anything lined up," despite the former Juventus and Real midfielder's obvious desire to return to management.
Zidane recently told TVE (h/t The Independent) he could make a quick return to coaching. However, The Independent's Miguel Delaney previously reported Mourinho won't be shown the door by United, despite losing two of his first four matches this season.
Tensions between Mourinho and executive vice-chairman Ed Woodward have been suggested since the Red Devils failed to land a centre-back in this summer's transfer market.
Woodward wouldn't back Mourinho on moves for Leicester City's Harry Maguire or Tottenham Hotspur ace Toby Alderweireld, according to James Robson of the London Evening Standard. He also blocked the sale of France international forward Anthony Martial.
However, Mourinho is still backed by senior figures at United, per Ciaran Kelly of the Manchester Evening News. His supporters will have been buoyed by United's 2-0 win away to Burnley last time out in the Premier League.
The result offered proof Mourinho can get his team back on track after humbling defeats to Brighton & Hove Albion and Spurs. There is still plenty of talent at his disposal, notably attackers Alexis Sanchez and Romelu Lukaku, as well as playmaker Paul Pogba.
Mourinho is under pressure to get the best out of these stars by producing a winning and preferably attractive playing style.
Perez may be concerned, and even a little irked, about the prospect of Zidane returning to the fray so soon. Yet the situation at United is far from simple, meaning it's likely the Frenchman will have to wait if he has his heart set on moving to the red half of Manchester.