On Monday, a report in The Age said Cornes had been informed by the club he could expect to be traded, or even sacked at the end of the season.
Primus denied the conjecture, insisting the 28-year-old was a required player at Alberton.
Cornes confirmed he had a scheduled meeting with the Power coach following the embarrassing loss to Collingwood a fortnight ago, but also dismissed reports his 223-game career at the club was over.
However, he did indicate that, like now-retired brother Chad, he wouldn't be guaranteed a game next season as Primus continues to rebuild the team with youth.
The premiership player, who still has two years to run on his contract, said he still expected to finish his career at Alberton, going as far as to say he would refuse to agree to a trade if his name was brought up in October's exchange period.
So far, Cornes is the only omission from the team that lost to Hawthorn by a club record 165 points, with the final 22 to be named on Friday afternoon.
It's the second time this season he's been sent back to Glenelg, but Primus denied it was a sign of things to come for the decorated veteran.
"Kane is a chance to get back in the team next week and the week after that," Primus said at training on Friday.
"I understand why that [speculation] is, but it's certainly not doomsday or the end of Kane's career just by him not playing this weekend.
"He's contracted here … and no decision has been made on his career.
"Like the changes we've made over the last couple of weeks, [Cornes has been omitted] because of form.
"We all know there are probably a few others in the same boat … and we'll still obviously have to drop a few out of the squad today."
Primus confirmed retiring ruckman Dean Brogan and out-of-favour forward Daniel Motlop would return to the team to play the Bulldogs.
It's been rumoured Moltop, who has only played 10 games for Port Adelaide this season, will not be offered another contract next year, but Primus said the 29-year-old would be given an opportunity to prove himself.
"His [Motlop's] form in the SANFL hasn't been outstanding, but he's been up and involved and North have been happy with how he's going about his footy," he said.
"He gets an opportunity to show he can still play at the level and what he can do."
The club has attracted heavy criticism following consecutive record defeats to the Magpies and Hawks, with Primus, the players, the recruiting staff, president Brett Duncanson and assistant coaches Dean Laidley and Jason Cripps all coming under simultaneous attack.
Primus said it was important the team made a stand against the Dogs on Sunday.
"We've all got issues going on in our lives, but our footy club has been dealt some pretty big blows in the last couple of weeks and we need to do something to stand up to that, not for each other, not just for our supporters but for our football club," he said.
"What we did last week, and what we did the week before is now in the history books.
"We've got three weeks to rectify to some extent what we did in the past fortnight."
Primus also confirmed the club was considering selecting SANFL midfielder Thomas Schwarz, son of Woodville-West Torrens' 1993 premiership captain Peter, under the father-son rule.
The St Michael's College student has been invited to observe day-to-day activities at Alberton ahead of the deadline for father-son nominations on October 7.
"We're not giving him [Schwarz] any guarantees, but we're impressed with his knowledge of the game and how he wants to learn and get better," he said.
Katrina Gill covers Port Adelaide news for afl.com.au. Follow her on Twitter: @AFL_KatrinaGill
