The 21-year-old Cat injured his left anterior cruciate ligament (ACL) in a tackling drill at training shortly before Christmas.
The Herald Sun reports that shortly afterwards, Menzel underwent the controversial LARS surgery, in which synthetic fibres rather than a muscle graft are used to reconstruct the ACL.
Geelong did not announce Menzel was undergoing a third reconstruction at the time.
The forward was cleared by his surgeon on Wednesday to start running and hopes to return to the Cats' VFL team by round one.
Menzel was able to choose LARS surgery because scans revealed he had only ruptured two-thirds of his ACL. His younger brother, Troy, who was drafted by Carlton in November, had LARS surgery as a 16-year-old.
"Because I'd already had two conventional reconstructions we weren't going to do a third one," Menzel said.
"Two in a row is hard enough mentally, three is too much.
"Fremantle's Anthony Morabito has had exactly the same thing and he's having LARS as well because you just can't do three (reconstructions) back-to-back pretty much."
Menzel said Geelong had kept his LARS surgery secret because it wasn't sure initially he would need another reconstruction.
But he said he never thought of retiring.
"A lot of bad things do go through your head but the LARS is such a quick turnaround, three months, which is not long in the scheme of things," Menzel said.
Menzel ruptured his right anterior cruciate ligament in the 2011 qualifying final against Hawthorn, and in his comeback match in the VFL last June tore his left ACL.
Nick Bowen is a reporter with AFL.com.au. Follow him on Twitter: @AFL_Nick