Jose Mourinho returned to Stamford Bridge for a second spell in June, and quickly spent big on Andre Schurrle and Marco van Ginkel, while Manuel Pellegrini announced his arrival with the signatures of Alvaro Negredo, Fernandinho, Jesus Navas and Stevan Jovetic.
Meanwhile, United boss David Moyes has failed with bids for Thiago Alcantara and Cesc Fabregas as he continues to try to bolster his central midfield, but Giggs is confident the current crop are talented enough to retain their Premier League crown.
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"The quality is in the squad. We showed that last year. Now we have to show it again. We won the league with those players so we are looking forward to the start of the season.
"If we sign someone - great. If not, we will just get on with it."
Meanwhile, Nemanja Vidic has dismissed suggestions that Sir Alex Ferguson's retirement has weakened the English champions, insisting United's winning mentality has not waned following Moyes' appointment.
"We respect everyone's opinion, but we know the players we have here," Vidic added. "We know what the expectations are. We are just focused on winning the title and we are not very bothered about what people say.
"We will show we can compete for the big trophies again, Champions League and Premier League. We don't have a problem with that.
"We never fight for our place in the media, we like to fight on the pitch and we'll do that again. Every season you have to prove you are good enough to play for this club.
"It's no different now. This club will always have big expectations, it doesn't matter who is the manager, who are the players, who is the chairman. It's always the same.
"Sir Alex was the biggest manager in football history, but this will continue to be a big club whoever the chairman or manager is."