The 2012 best and fairest winner wants to head north to be near his father, who has battled cancer in recent years.
Beams' younger brother Claye plays for the Lions but the Lions have baulked at the idea of trading a ready-made midfielder to the Pies along with draft pick No.5.
The Suns consider the situation to be a one-horse race and believe Beams will become a Lion if a trade gets done.
"It's very interesting. Doing business a lot and knowing his manager Paul Connors pretty well and how he operates, he's a great manager, and when he says this one's not for you, it certainly means this one is not for you," Suns' list manager Scott Clayton told 3AW on Tuesday night.
"I think if anything gets done it will be with Brisbane.
"Clearly we'll have one eye on it but I wouldn't think that it will be us."
Complicating matters is the deadline the Magpies have given the Lions to present them with an acceptable trade option by.
Collingwood CEO Gary Pert told the Herald Sun on Saturday that the Pies won't entertain offers from the Lions after 5pm this Friday.
If they haven't agreed to a trade by then, they will "close down discussions" and seek to "move forward with other trades and other opportunities".
Meanwhile, the Suns will sit down with ruckman Daniel Gorringe this week to see if his position has changed after the removal of coach Guy McKenna.
The 22-year-old has requested a trade back to South Australia but the club has not spoken to him since McKenna was sacked (Gorringe has just returned from overseas).
Clayton said the Suns had spoken with Port Adelaide – Gorringe's preferred club – but talks had not progressed.
"He said to us a couple of weeks ago he'd like to move on," he said.
"He's a contracted player and we'd certainly like him to stay.
"He has mentioned Adelaide, the city of, and his preference being Port Adelaide, who has initiated some conversations with us that we haven't taken anywhere.
"Dan has been overseas, he got back today [Tuesday], so we want to sit down and have a chat now that our coaching situation has changed and see where he's at.
"But he's certainly mentioned that Port Adelaide is where he'd like to go."
Clayton said he expected Gary Ablett's contract extension to be finalised when the two-time Brownlow medallist returned from overseas.
