Other clubs have paid similar tributes, including West Ham for Bobby Moore, Cologne for Lukas Podolski and AC Milan for Paolo Maldini - the Italian club will reportedly only reissue the no.3 jersey if one of the legendary defender's sons plays for them.
When asked by MUTV if United should retire his number in the wake of his retirement, Giggs replied: "No. There are obviously special cases but it just depends on the club really. I don't think it's [right] for United where they constantly churn over great players.
"I haven't thought about who will take over the number 11 shirt - that's a good question.
"They're under pressure, aren't they?!" he joked, before adding: "I look forward to seeing who takes it and wish them all the best."
Giggs also recalled how he gained the shirt number he made his own during his glorious 23 years in the United first team.
"I wore number seven for a few games, when the shirts were just numbered one to 11. But 11 was usually worn by the left winger so it really just happened [that I kept it when squad numbers were introduced]."
MUTV is going HD this month and you can see every United pre-season match live on the channel, starting with LA Galaxy on 23 July followed by games against Roma, Inter Milan and Real Madrid. Find out more at www.manutd.com/joinmutv.