David Moyes' men overcame a 2-0 deficit from the first leg of their Champions League last-16 tie with the Greek champions after a hat-trick from Robin van Persie, with Giggs also starting and playing a key role in the victory.
Goal's special report on Wednesday looked at how Giggs was potentially being considered as a replacement for under-fire manager Moyes, who eased some of the pressure on his shoulders with the triumph over Olympiakos.
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"I hope so, yeah, I have probably not played as much as I would like in the last few months but hopefully," the Welshman told reporters.
"I think the team [against Olympiakos] had a mixture of a lot of things: pace, experience, power. That's what Manchester United is about and we showed that. We showed what we are capable of."
However, Giggs did warn that United's poor performances this season could lead to a long-term decline if the club are not careful.
"Well, you can see why people are saying that because we haven't produced it this season on a regular basis," Giggs said.
"I know from experience what these players are capable of and a lot of them have been written off. I think there is a lot of quality within the dressing room. We showed it [on Wednesday] and we have to show it more consistently.
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