Peters is seeing his specialist within the next few days who will decide whether or not he has the all-clear to fly again.
"He's hopeful by then [after the appointment] he would have received that clearance – he's gagging to move outside of the bounds of [his home]."
Peters has been confined to his Auckland home since the operation but has been working and has maintained regular contact with his staff.
"He is seriously looking forward to getting that clearance so he can get back here [to Wellington]."
Peters has not spoken publicly since the operation and did not respond to the Herald's request for comment.
But in a video he posted on Facebook he thanked those who had sent him messages of support.
"Things [will] soon be getting back on track."
Peters is due to go to a KiwiRail event this Friday, but whether or not he gets to go "remains to be seen" depending on what the specialist says.
As he was confined to his home last week, he missed the funeral of former NZ First MP Pita Paraone.
Peters' spokesman said the Deputy Prime Minister was upset to miss the event.
"They had a very, very long history. They were very close."
Ardern told the post-Cabinet media conference today that when she last spoke with Peters regarding some "bits-and-bobs" he was in "good spirits".