Galvin this weekend told Canterbury officials he had been sold on their vision for Belmore, with the Wests Tigers five-eighth to knock back an offer from rivals Parramatta.
An immediate release from the Tigers is possible within days, provided a six-figure transfer fee for the final 17 months of his contract is agreed to.
"What I understand of the situation right at the moment is that Lachlan Galvin has expressed his desire to play with the Bulldogs," Gould said on Nine.
"We still haven't closed off on a deal yet, and there are still some things that have got to be worked out with the West Tigers.
"I would hope that in the next 48 hours we have far greater clarity."
Galvin's move will put a full stop on the lengthy saga surrounding his future, which began when he requested a release from the Tigers before his debut last season.
The 19-year-old officially informed the joint-venture last month he would not re-sign beyond the end of 2027, before he was given permission to talk to rivals.
Parramatta had also been favourites to secure his services, given he played juniors for the club in the Harold Matthews competition.
But his decision to go to Canterbury looms as a significant coup for Gould, who just weeks ago suggested the Bulldogs weren't interested in the teenager.
Where Galvin plays at Canterbury remains a point of interest.
Halfback Toby Sexton is off contract at the end of this year, and negotiations are yet to begin around a new deal.
Galvin remains untested as a controlling halfback, while Canterbury five-eighth Matt Burton has only played nine games in the No.7 jersey.
There is a suggestion Galvin could play as a lock, or Burton could shift to the backline.
But Canterbury would be unlikely to make significant changes given their 9-2 start to 2025 has them first on the ladder.
"He's very versatile," Gould said of Galvin.
"He's played fullback, five-eighth, halfback. The first time I saw him play, I thought he'd end up a back-rower.
"I know he's going to be a very good player and we'd like to be a part of his development
"He's extremely gifted, he's a creative player. He's big and tall ... what I know is you win comps with talented players.
"And our aim is to be competitive to win premierships. And Lachlan Galvin is a player you want at your club down the track."
Galvin's decision means Parramatta must continue their search to replace Newcastle-bound Dylan Brown.
The Eels had pushed hard to sign the teenager, with Mitch Moses selling him the vision of leading the club within four or five years.
But it's believed the club did not want to get into a bidding war with Gould and the Bulldogs.
Other options remain on the market, with clubs keeping a close eye on Melbourne's Jonah Pezet if Jahrome Hughes recommits to the Storm for 2027 and beyond.
Meanwhile, Galvin's eventual exit from the Tigers will end a sorry chapter for the club, given the Campbelltown junior represented one of their best young talents.
His final act could well be dropping a ball over the line late in last week's loss to the Rabbitohs, effectively costing the Tigers the game.
Fellow teenager Latu Fainu is expected to be available to return from a hand injury against North Queensland next week, and will now have the chance to become Jarome Luai's long-term halves partner.
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