Frontrunners for Butters' services, the Bulldogs loom as the logical move for the free agent because he grew up as a die-hard supporter of the club, as well as his family's links to the west of Melbourne.
Beveridge refused to be drawn on a reported recent meeting with Butters, but reiterated the Bulldogs were desperate to land the gun midfielder.
It is almost accepted the 25-year-old will leave Port at season's end and return to Victoria after eight years.
Richmond, Geelong Collingwood are among other clubs  trying to recruit Butters with monster offers.
But that doesn't mean Beveridge believes the AFL should be more open about player movement.
NRL players can sign for rival clubs more than a year in advance but continue playing for their current team.
"I don't want to go down the NRL track," Beveridge said on Wednesday.
"It's a really difficult thing club-wise to know that one of your players is leaving.
"Ultimately, they'd be treated a bit differently. I mean you don't want to, but if they're not your player beyond that year, you can't help be emotional about it.
"If we're after a free agent or really hunting a player who we think might be able to come in a trade, the senior coach has to be involved.
"Our club have declared we want Zak to come to our club, and ... I'm obviously involved in it.
"But I'd rather it not be declared, and I think secrecy around it is important for club land."
Butters grew up idolising Bulldogs great Brad Johnson, and the club considered picking him in the 2018 draft.
The Bulldogs ultimately selected Bailey Smith with their first pick, with Butters sliding to No.12 and chosen by the Power.
Bulldogs captain Marcus Bontempelli has been trying to convince Butters to pick the club.
"Marcus, and some of Marcus's teammates, are quite naturally drawn to Zak," Beveridge said.
"They played in the state (of Origin) team together (in February), so he's developed some relationships with some of the other boys who played in that game."
After winning just one of five matches, the Bulldogs are on a three-game winning streak ahead of Thursday night's clash with Adelaide at Marvel Stadium.
The Bulldogs secured a thrilling six-point win in Adelaide over the Crows in round two.
But Beveridge is on guard after the Crows won a shootout at Docklands in round 18 last year.
Adelaide veteran Taylor Walker (suspension) will be replaced by towering key forward Riley Thilthorpe, while Luke Pedlar comes in for Callum Ah Chee (hamstring).
The Crows will continue taking a cautious approach with Izak Rankine, who will miss another week with a calf injury.
"They came over (last year), we were aware of some of their threats, and it was one of those games where we got beaten by what we knew," Beveridge said.
"So we go into this game understanding who their key playmakers are, and we'll need to make sure we don't allow them to play too well."
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