Goal has learned that people behind the scenes at Old Trafford expect the 40-year-old to be installed as boss before the end of the season, in the event of Moyes' dismissal.
At Monday's press conference Giggs was prevented from responding to a journalist who asked whether his aim is to eventually become United's manager, but the player dismissed reports which suggest there is a rift between himself and the Scot.
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“As a player you want to play all the time, but I know I probably won't play every game.
“The last time I played was probably the first time in six or seven weeks but we've got a lot of players to choose from and as you see in the performance against Olympiakos I'm always ready to come in and play and that's what you've got to do, not sulk because you're not playing you've got to come in and be ready to play for the team.
“The players tomorrow if they've not been playing have got to come in and perform.”
Following Giggs’ response, Moyes interjected jokily: "I'm doing his yoga classes now, maybe that will help me.”
Manchester United host Bayern Munich in their Champions League quarter-final first leg on Tuesday evening.
The two sides head into the fixture with contrasting campaigns. While Bayern have already won the Bundesliga, United find themsevles far behind the title pace and will record their lowest-ever points total in the Premier League this term.
But Giggs has rejected the idea that United are approaching the contest as underdogs.
“Obviously Bayern are a fantastic team. They are the holders. Pep Guardiola has took over, added a few new players and obviously they are a very strong team,” he said.
“And like you say, probably favourites in most people’s eyes.
“But we’re Manchester United, it’s at Old Trafford and we have seen so many great nights in Europe especially.
“As players, we don’t see ourselves as underdogs. We see ourselves as Manchester United playing at home in the Champions League and we can’t wait.
“These are the games you want to be involved in as a player. We’ll go out and try and win the game, it’s going to be tough but it usually is in the quarter-finals of the Champions League, but we’re confident, we’re looking forward to it.”