Manchester United last won the competition back in 2008, when Sir Alex Ferguson was in charge.
Giggs was part of that team – as well as the one that reigned supreme in 1999 – and knows a thing or two about life on the European stage.
However, the former Wales international thinks that, though Jose Mourinho’s side have hit the ground running in the Premier League, they do not have the players to win Europe’s top club competition just yet.
Yet he does think the signing of Real Madrid star Gareth Bale would be enough for them to land the prize.
“You look at the current Manchester United team and you wonder if they can they win the Champions League?” he told Sky Sports.
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“Have they got the players to win it?
“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.”
Giggs also said he thinks Real Madrid and Ligue 1 giants Paris Saint-Germain are the teams to beat.
And he added he thinks Barcelona are weaker without Neymar in their ranks.
“Apart from Real Madrid, obviously you’ve got PSG, who have made big intentions this year, but it could be quite open otherwise with Barcelona losing Neymar and not making the best start,” he added.
“You have to look at Real Madrid, what they’ve done after the last two years and the players they’ve got, as the team to beat.”