He told BBC Radio Cambridgeshire: "The operation was a success, but I need to take it slow and make sure I get everything right.
"The aim is to be fully fit by the start of the season and I should be raring to go well before that."
He added: "I'm taking it a bit slower than the others but the physio is doing a good job. I'm just happy to be back running around again."
Competition for a starting place in the centre of defence will be high with defenders Kelvin Langmead and Mark Little both signing for Posh over the close season, adding to Zakuani, Craig Morgan and Ryan Bennett
"[Competition] keeps the team healthy and doing well," said Zakuani.
"I wouldn't say any two [of the defenders] are very similar and I'm sure that whoever's picked will build a good partnership.
"We've got five good centre-backs and, if you include Charlie Lee, there's another who can play there.
"It's up to two to stand out."
Source: BBC Sport
Source: BBC Sport