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It has been a busy start to the NAB AFL Free Agency Period for the Roos, who also secured Carlton spearhead Jarrad Waite as an unrestricted free agent on Friday morning.
Higgins' manager, Bruce Kaider of One Management Group, told AFL.com.au on Tuesday his client had told the Bulldogs it was in his best interests to continue his career at a new club.
Kaider said North Melbourne and another club, which he preferred not to name, were in the running to sign Higgins, but AFL.com.au reported that it expected Higgins to be at Arden Street from 2015.
Earlier this year, Higgins put contract talks with the Bulldogs on hold to the end of the season after refusing to accept a new two-year deal.
It is believed Higgins will join the Roos on a three-year deal that has a trigger clause for a fourth season.
The 25-year-old's decision to leave Whitten Oval is also understood to be based on the desire for a fresh start, but Bulldogs CEO Simon Garlick has refused to rule out matching the Kangaroos' offer.
"We've clearly got both the capacity in our salary cap and the capability from a financial view to match, we think, any offer that Shaun's going to get," Garlick told NAB AFL Trade Radio on Thursday.
If the Bulldogs do match the Kangaroos' offer, Higgins would be forced to find a new home through the draft period.
Carlton, Geelong, Greater Western Sydney and Richmond were among the other clubs to express interest in Higgins this year, with the Blues emerging as the Roos' greatest challenger before bowing out of the race last week.
Higgins was pick No. 11 in the 2005 national draft and played 129 matches for the Bulldogs and kicked 128 goals.