Zidane has been out of a job since leaving Real Madrid at the start of the season.
After failing to win any of their past four games, United fought back from two down to beat Newcastle 3-2 on Saturday.
"I think they thought in the morning, 'Is he going to be there?"
The game came amid media reports of Mourinho's future being on the line, with one paper saying he would be fired this weekend regardless of the Newcastle result - a claim denied by the club.
According to The Sun, players gave their opinions on the team's problems and Mourinho asked Pogba over what changes needed to be made.
Manchester United's Portuguese manager Jose Mourinho gestures during the English Premier League football match between Manchester United and Newcastle at Old Trafford in Manchester, north west England, on October 6, 2018.
So often criticised for preaching a cautious approach, it was only when Mourinho's men threw caution to the wind when 2-0 down that they began to look like the United of old. Six minutes later, Anthony Martial cut inside after swapping passes with Paul Pogba to equalise with a venomous low shot.
The game would end in a 3-2 comeback victory for United, the kind Old Trafford witnessed many times under Alex Ferguson.
"I think they saw today we tried everything, and we came back and from the mental point of view it's a very important three points".
"At halftime we were losing 2-0 and the fans were magnificent to the team and that is fantastic", he said, adding that he would have preferred not to hear his own name.
"We all know one swallow doesn't make a summer", he told the BBC.
Next up for Manchester United is a visit to London to take on Chelsea at the Stamford Bridge.
Sanchez's victor also saw United supporters, who had been muted in their backing for Mourinho to that point, sing his name out loud around Old Trafford.
Woodward will be mulling over those figures, particularly as the compensation would drop to just £10m if he stays in place until the end of the season and United don't qualify for the Champions League.