Speaking on AFL.com.au's Gillette Trade Radio, Carlton recruiting manager Shane Rogers said the Blues had offered Betts a "pretty decent" deal and hoped he would stay.
Betts, 26, is a restricted free agent, meaning the Blues have the right to match any offer placed in front of him.
But Rogers said Betts and his manager had delayed talks for most of the season.
"The rumour is Adelaide and North have both put an offer in," Rogers said.
"We haven't heard form either of those clubs. We obviously think something's up. We assume he'll let us know soon."
Rogers said the rival offers were substantially more than Carlton's, but it was not prepared to compromise its pay scale.
He said Betts has every right to look for a longer deal that would secure his future.
One player Carlton is confident of getting is Collingwood's restricted free agent Dale Thomas, with the Magpie successfully getting through some medicals.
Rogers said the Blues had put in an offer for Thomas and expected something to come to light over the weekend.
"We're waiting to hear back from his manager to see what Dale's thinking, but we're quietly confident that we might be able to do something there," he said.
"We've put him through two or three medicals. We're comfortable with what the doctors have told us."
Getting Thomas would fill one of four areas Carlton has addressed as key in its off-season plans.
It is after a strong-bodied midfielder, a centre half forward, centre half back and an outside runner.
Rogers confirmed the Blues had spoken to Greater Western Sydney's Taylor Adams, had considered Sydney Swan Jesse White, who was now down the pecking order, and were out of the race for Brisbane Lion Brent Staker, who he believed would re-sign with his current club shortly.
Despite a desire to land the number one draft pick and power forward Tom Boyd, Carlton will not deal Matthew Kreuzer or Bryce Gibbs to GWS under any circumstances.
Rogers said they were reluctant to let contracted ruckman Shaun Hampson go, but would wait to see if an offer came from interested rival Richmond.
Heath Scotland is likely to make a decision on his playing future next week.
