The Red Devils have made a flawless start to their Premier League campaign under their new manager after securing back-to-back victories.
United were 3-1 winners against Bournemouth in their league opener at the Vitality Stadium last weekend courtesy of goals from Juan Mata, Wayne Rooney and Zlatan Ibrahimovic.
The 34-year-old summer signing scored twice on Friday night as the Red Devils eased to a 2-0 victory over Southampton at Old Trafford in their first home game of the season.
United are currently at the top of the Premier League table as Louis van Gaal’s replacement Mourinho attempts to win his fourth English title but first as Red Devils manager.
Asked if he believes United will be crowned Premier League champions this season, Giggs told Sky Sports: “I do.”
Giggs added: “They’ve got a huge chance because of the options they’ve got. I think they’ll win it.
“They have a manager who knows how to win the Premier League.”
The Red Devils will make the trip to Mike Phelan’s promoted side Hull City in their next Premier League game next Saturday.
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