The Real Madrid star, who moved to the Bernabeu from Tottenham Hotspur in 2013, was heavily linked with a switch to Old Trafford in the summer.
The Red Devils will return to the Champions League after a 644-day absence this evening when they take on Basel on home soil, but Giggs believes that the team are not yet good enough to go all the way.
"You look at the current Manchester United team and you wonder if they can they win the Champions League? Have they got the players to win it?" Giggs told Sky Sports News.
"They're probably a little bit short at the moment. You've got Paul Pogba and Romelu Lukaku, if he fulfils his potential, Marcus Rashford, David de Gea, a world-class player, and then if you add somebody like Gareth Bale to the mix, that's when you talk about United having Champions League expectations.
"Obviously, Mourinho has won the trophy before so we're going to be there or thereabouts, but whether we've got the players to go the whole way, I don't know."
United will also face CSKA Moscow and Benfica in Group A.