The Age newspaper reported on Wednesday that former coach Mark Thompson had pushed for the club to re-sign the veteran duo, who are aged 33 and 30.
With Thompson having quit the club since then, it was reported that several Geelong administrators were unhappy he was allowed to influence such a key list-management issue.
But Balme has played down those suggestions.
"While you can debate when blokes should retire, we're extremely happy for both Darren and David to play on," he told SEN Radio.
"We want them to stay, they want to stay, and we've got to make the most of it."
Already reeling from the loss of Thompson and Brownlow medallist Gary Ablett, who has signed with Gold Coast, the Cats were shocked again on Tuesday when assistant coach Brendan McCartney walked out on the club.
McCartney, who had a four-year contract to head up Geelong's development program, has moved to Essendon where he will work under James Hird.
"Brendan had indicated he would like to run our academy long-term," Cats chief executive Brian Cook told SEN's Morning Glory program.
"He's had a change of mind over the past couple of months, particularly after his interviews with Port Adelaide for their senior job - I think he got pretty close to that.
"It stirred his motivation to once again be a match-day coach in the box, as distinct from working with the young recruits."
Given Thompson has been strongly linked to Essendon in the past month, he has been implicated in McCartney's decision to join the Bombers.
However, the Cats are refusing to buy into such theories.
"There may have been a discussion that I'm not aware of between Essendon and Bomber about whether McCartney was any good, which of course he is," Cook said.
"But I don't believe in any way that Mark Thompson has lured McCartney to the Bombers. Brendan McCartney guaranteed that to us yesterday and we take him on his word."
Cook has admitted he would not be surprised to see Thompson take on a position at another club, despite the fact he left Geelong citing exhaustion.
"My gut feel is that he may end up in a part-time role at a football club and most likely Essendon, but I don't know," Cook said.
"I certainly believe that he won't go back into footy full-time."
Geelong is aiming to announce its new coach within the next month, with former Cats players Ken Hinkley, Brenton Sanderson and Mark Neeld the current front-runners.
"We're not interviewing lots and lots of people," Cook said.
"Most of those initial interviews have finished and we'll be having second interviews next week and the week after.
"We'll make sure that we have a decision before the players come back."
