Cherry-Evans, a Redcliffe junior, has publicly stated this year will be his last at the Sea Eagles as he weighs up playing on in 2026.
The 36-year-old asked for a release in 2023 from his Sea Eagles contract to move to a Queensland club, which was denied.
AAP understands that club was the Dolphins.
The Sydney Roosters are considered to be one of the two front-runners as they have both the salary-cap space for Cherry-Evans and are based in Sydney, which means the Queensland captain would not need to uproot his young family.
The appeal of the Dolphins, on top of being his old stomping ground, is enhanced by his parents living in the Redcliffe area.
Both clubs have played a straight bat when asked about signing the 335-game veteran.
"As a business, you've got to look at it. I say we'll get to it when we know a bit more and decisions get made," Roosters coach Trent Robinson said last month.
Dolphins boss Reader, speaking on Wednesday ahead of Friday's night's home clash with Melbourne, made it clear the club could afford Cherry-Evans.
"If he makes a decision that he is interested in coming to Brisbane, we are obviously going to talk to him," Reader said.
"If that was to happen and he did want to come to Brisbane, I am sure we could make it happen.
"Does he want to come back to Brisbane for a couple of years to where his mum and dad live? Or does he want to stay in Sydney? They are questions people need to have Daly answer."
The Dolphins' top 30 is settled for this year. Next season is a different story, with 24 top-30 players re-signed and development list prop Elijah Rasmussen.
The club has at least seven players off-contract, including half Sean O'Sullivan and forwards Mark Nicholls, Kenny Bromwich, Josh Kerr and Felise Kaufusi.
The Dolphins clearly can't keep them all and sign Cherry-Evans.
"The cap is quite complicated. You have kids coming through, upgrades and spots on the development list," Reader said.
"There's a salary cap and positions in the squad we are working through every day,
"Those things will take care of themselves as the season goes on. If guys are playing good football they get rewarded with contracts."
Meanwhile, Reader said the club had not considered making a play for Wests Tigers five-eighth Lachlan Galvin, who will be available for the 2027 season onwards only at this stage.
"Is that another one for us? We must have an unlimited salary cap," Reader chuckled.
"But that's not something we are involved in. If he's on the market for 2027 that is not really something the Dolphins will be pursuing at this stage. We haven't had a conversation about Lachlan Galvin."
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