Zidane has been out of work since leaving Madrid at the end of last season, just days after becoming the first manager to win three successive Champions League titles.
Speculation had linked the France legend with a switch to Old Trafford amid growing uncertainty regarding the future of Mourinho.
Pressure is mounting on the Portuguese boss following numerous reports of fallouts with players, growing discontent at the team's style of play and the 19-point chasm which separated his side from champions Manchester City last season.
However, the Daily Mail reports that Mourinho retains the full backing of the United board, even after Sunday's 3-2 defeat at the hands of Brighton & Hove Albion.
Mourinho won the Europa League, EFL Cup and Community Shield in his first season as United boss, but failed to pick up any silverware last term.