The free agent made his debut for the Saints in 2016, having played 115 games over the span of his career since.
After an injury interrupted few seasons, the 25-year-old managed 18 games in 2022 and has featured in both of St Kilda's first two matches to start the season.
With his current contract set to expire at the conclusion of the season, Twomey believes that Gresham will be in demand around the competition.
“He shapes as one of the most in-demand free agents in the game this year,” Twomey said on SEN Breakfast.
“He's a quality player and he's obviously back to some of his best this year with the last couple of weeks with St Kilda.
“Reports today in Inside Trading that he's going to wait until deeper in the season before focusing on his free agency call.
“I think he's going to be very sought after.
“I don't think St Kilda are in a rush at the moment, either.
“There's a period as well with the new coach where he gets to see what the group has, what it doesn't have and how it looks for the rest of the season.
“He'll qualify as a restricted free agent, so they'll be able to match the bid.
“But there hasn't been a contract offer tabled yet.”
The Saints have gotten off to a strong start under Ross Lyon, winning both of their opening two matches against Fremantle and the Western Bulldogs. Gresham played in both, averaging 17.5 disposals and 2 goals.