Beams is contracted until the end of 2015 and a suitable trade would need to be organised before he was able to leave.
He is not eligible to become a free agent until the end of 2016.
Collingwood director of football Rodney Eade said the Magpies would look at ways to make it possible for Beams to spend more time with his family while continuing to play with Collingwood.
"We want Dayne to stay," Eade said.
"We understand his personal situation and will be working with him and his management, as we do all our players, to find an outcome that may give him more time with his family and remain a Collingwood player for 2015 and beyond."
Beams, 24, grew up on the Gold Coast and his brother, Claye, plays for the Brisbane Lions. The Magpies selected him with pick No.29 in the 2008 national draft.
He made his debut in round two, 2009 and has played in 110 games with the Magpies including the 2010 premiership, where he performed well under Mick Malthouse.
Both Queensland clubs were reserved with their reactions.
The Lions said they were "surprised" at the news, and wanting to respect Collingwood's position, and this weekend's Grand Final, would let the dust settle until next week.
However, with well over $1 million available in the salary cap and fitting coach Justin Leppitsch's desire to recruit A-grade talent, he appears a perfect fit.
Gold Coast would not rule out a pitch for Beams, but said it would also not consider anything until next week's trade period began.
"We will look to strengthen our list in line with our list management strategy, and that includes looking at all options during the free agency and exchange periods," Gold Coast football operations manager Marcus Ashcroft said.
"We are not in a position to discuss individual players, until those time-frames present."
Beams flourished in Collingwood coach Nathan Buckley's first season in 2012, winning the club best and fairest, being named All Australian and polling 19 Brownlow votes.
Beams only played eight matches in 2013 due to injury but returned to form this season being alongside Scott Pendlebury as Collingwood's best player.
On Monday night he polled 16 Brownlow votes – equal with Pendlebury and is a likely placegetter in the club best and fairest this season.
Former Collingwood skipper Nick Maxwell told SEN he was surprised when he heard the news that Beams wanted to return to Queensland.
"He's a really important player to the footy club," Maxwell said.
It's disappointing but there is probably a fair bit of water to go under the bridge before we find out more. They are in a tough predicament because he is so important to that team and really popular amongst the boys."