The Catalans made offers for both defenders earlier this summer, but Gerardo Martino has claimed they will no longer sign a centre-back
The Liga champions were prepared to pay €25 million for the Brazil international, but Chelsea were holding out for double that figure, while Barca's offer for Agger was deemed insufficient by Liverpool, prompting the Catalans to end their pursuit of a new defender.
"A new centre-back? I'm happy with the team I have. There's always the January window if we need anything. Last year's problems in defence were the result of injuries. We have enough options if everybody's fit," Martino said at a press conference.
"Puyol is on schedule with his recovery process. We are awaiting his return and expect him to be match fit again come September.
"We have Puyi in defence, Gerard Pique, Javier Mascherano, Marc Bartra and even Adriano. If someone gets injured, the January transfer window is only months away."
Barcelona start their 2013-14 Liga campaign on Sunday as they host Levante.