His manager, Ned Guy, has said that a bigger pay packet was one of the incentives for Betts to leave.
"That’s definitely part of it, but it’s also playing out the rest of his days in a good environment," Guy said on SEN this week.
"He loves the Carlton footy club, he probably didn’t have his best year this year, but that’s one of the factors that we will certainly take into consideration when we make a decision."
Carlton confirmed Betts has notified the club of his intention to explore free agency.
"Betts and his management met with Carlton’s football department this morning," a statement said.
"Carlton recognises that as a restricted free agent, Betts may consider offers from rival clubs.
"The club will not be making any further comment at this time."