The Bohemians defender, out of contract with the Irish club, has been looking for a new club in England with Luton Town also strongly interested in the former Fulham man.
Bohs boss Pete Mahon felt convinced the stopper would finally opt for a switch to the South Coast, with Sean O'Driscoll a firm admirer of his talents.
"I spoke to Shaun yesterday," Mahon told setanta.com. "Personally, I'd be amazed if he signed for Luton Town.
"I heard on the radio today that he'd signed for Luton but I'd still say he'll sign for Bournemouth."
Maher actually signed on a non-contract basis but is expected to tie up a longer contract next week.
