Beams wants a move to the Lions to be nearer his father,who has battled cancer,and play alongside his brother Claye.
But likewise,Collingwood want more than the Lions'initial offer of their first-round draft pick,currently No.4.
Beams finished third in the Magpies'best and fairest voting.
Monday could open with Hawthorn confirming they have signed Melbourne defender James Frawley under free agency.
A video interview briefly appeared on the Hawks website on Saturday morning,featuring Frawley being interviewed in a Hawks top,before it was removed.
The Magpies will also learn at Monday morning's father-son bidding meeting what they will have to give up for Darcy Moore.
Carlton and the Western Bulldogs could also bid for Moore,who is the son of two-time Brownlow Medallist Peter.
If that happens,Collingwood will have to use their round-one draft pick at No.8 to secure the key position player.
Other players featuring in trade speculation include:-
* North Melbourne onballer Levi Greenwood. The Kangaroos are determined to keep him.
* Former Melbourne forward Mitch Clark,who wants to make a comeback. Geelong are his preferred destination.
* Sydney's All-Australian defender Nick Malceski. He could use free agency to join Gold Coast.
* Adelaide midfielder Patrick Dangerfield. There is ongoing speculation about a potential blockbuster trade,but he seems more likely to remain a Crow.
* Collingwood veteran Heritier Lumumba. He is set to join Melbourne in a trade.