"There's still some fragments off the bone and the tendon's still a bit how's it going."
However the hard-running big man remained hopeful of taking part in three-match series against England, beginning on October 23.
"I'll catch up with Mooks (Kearney) this week to have a chat and see how we go for the tour. I'm hoping I can pass medicals next week," Taumalolo said.
"Any time I get an opportunity to pull on the black and white jersey, I'm more than happy to take it. I want to play for New Zealand."
Despite his knee problem, Taumalolo was one of the Cowboys' best in his three separate stints on the field.
He spurned a lucrative deal from the Warriors earlier in the year to win a premiership in Townsville, and he predicted more success for the relatively youthful side.
Skipper Johnathan Thurston is the only player over the age of 30, and the entire 17 will return to the fold next season.
Asked whether the Cowboys had an opportunity to create a modern-day dynasty, Taumalolo said: "Definitely. Obviously Johnno's hitting the back end of his career but we've got young players around him like Michael Morgan, Jake Granville and Kyle Feldt."
Should Taumalolo be ruled out of the Kiwis' tour, he joins a lengthy list of high-profile stars to miss trip, including key men Shaun Johnson and Kieran Foran.