It's believed Hainsey is willing to sign a one-year contract worth less than the $4.5 million annual salary cap hit he had with the Winnipeg Jets last season.
Hainsey, 32, is arguably the top free agent defenseman in the market, but has yet to sign a deal with a club.
Last week, Hurricanes GM Jim Rutherford admitted that he's close to signing an "upper-tier guy" to a one-year deal, but needed to move a body off of his roster before locking down the mystery player to a contract.
"There's one guy that has said he will take less on a one-year contract to come to us, because he likes our team and he'd like to play here," Rutherford told 99.9 The Fan, Raleigh's ESPN affiliate at the time. "I've been continuing to work on ways to do that.
"We're going to have to move a player out before we're able to add a player, and at this point in time I haven't been able to do it, but the player is still waiting patiently."
Hainsey picked up 13 assists in 47 games with the Jets this past season.