The Blues announced on Thursday morning that Betts and his management had told them he wanted to look at his options.
"Carlton forward Eddie Betts has today notified the club of his intention to explore free agency," they said.
"Betts and his management met with Carlton's football department this morning.
"Carlton recognise that as a restricted free agent, Betts may consider offers from rival clubs."
Betts' decision comes as no surprise, following widespread speculation for several months about his future.
The 26-year-old has played 184 games for the Blues since his 2005 debut and led their goalkicking in 2010 and last season.