"If you play well and are lucky you have a good chance of going far, but even then I think there are eight to 10 teams who could win it this year," the United striker told UEFA.com.
"Once you get to this stage of the competition you know that there are not going to be any easy matches," said Giggs, who was in the United side that beat the Greeks 7-2 on aggregate the last time they met in 2002.
"It's hard to believe that was 12 years ago," he added.
"I remember the home game in 2002 very well - probably because I scored twice.
"This time I think it will be a much more competitive and experienced Olympiacos, they did well in their games in the group stages.
"We know this match is going to be a tough tie, Olympiacos have a strong team."
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