The proposed one-year deal, which has been presented to Smith’s manager, Isaac Moses, would take the games record holder close to the 400 mark.
Melbourne’s chief executive Dave Donaghy told the Herald Sun that an offer had been made to the Sydney-based Moses.
Smith was under an injury cloud earlier in the week after leaving last Friday’s clash with the Rabbitohs in the 73rd minute due to a pain in his heel.
But the veteran hooker was cleared of serious injury and is expected to lineup this weekend against the Sharks.
“He did not require scans because he pulled up so well,” Storm football director Frank Ponissi told the Herald Sun.
“The injury is a tendon irritation to his toe.”
Ponissi added that Smith was being effectively managed but the club’s medical staff were particularly optimistic about his latest setback.
“He gets managed well regardless of any injury just because of his age and so on … if it was recurring I’d imagine they’d look at that,” Ponissi said.
“Given the profile of the player, who he is and how important he is, and our medical staff always err on the side of conservative rather than aggressive.
“I’ve been pleasantly surprised how at ease they’ve (medical team) been on the injury since Friday night … it’s been good news after good news after good news, since then.”