The 23-year old Australian defender comes out of contract with the Edinburgh club at the end of the season and is trying to win an improved deal after rejecting Rangers in the recent transfer deadline.
However, Jambos boss John McGlynn has made it clear that the Tynecastle outfit are not in a financial position to be handing out lucrative contracts and hopes that McGowan realises that and remains at the club to continue his development.
"It's negotiations, we all know how it works,” he told the Daily Record.
"They (McGowan and agent) want a bit more but Hearts are having to cut back and haven't been paying what they previously did.
"That's why we are where we are so if players are looking for the money they were getting 18 months or a year ago, it's probably not going to happen.
"We have to cut our cloth and break even. But the best place for Ryan to continue his development for the next two or three years is Tynecastle.
"I don't see him being distracted by contract talks, because negotiations have been going on for a while."