Reports on Sunday morning emerged that, while Smith would give the Storm another chance to persuade him, the prospect of playing number nine in a successful team under Trent Robinson was leading the race for Smith.
Speaking on the YTKR podcast though, Smith said more clubs have popped up with offers in the last couple of days following other developments in the transfer market.
Smith confirmed the Tigers, Panthers and Eels have all entered the race for his signature.
That comes on the back of news Reed Mahoney has signed a four-year deal to shift to the Canterbury Bulldogs from 2023, while Apisai Koroisau's place at Penrith is under the pump as the premiership-winners attempt to balance their salary cap.
"A few clubs have come up in the last two days to try and offer me," Smith said.
"The Tigers, the Roosters, Penrith had a little dabble because of the Api thing, the Storm obviously, the Titans and Parra just had a shot."
Seemingly hinting that he may play for one of the three reported front-runners though in the Roosters, Storm or Dolphins, Smith paid a glowing tribute to the three coaches at the clubs, saying it gave him confidence that all three were interested.
"It's pretty good, but for me it's hard to turn away from Wayne Bennett, Trent Robinson or Bellza (Craig Bellamy) and that's what made me the happiest about this whole thing - those coaches want me. They know their footy. They know their players. I take a lot of confidence out of that."
Smith will remain at the Storm in 2022, with reports suggesting the club will still have another shot to keep him for 2023 when he returns to Melbourne this week.
It's widely acknowledged though that Smith wants to play as a starting hooker, and with Harry Grant tied to the club until at least the end of 2023, it means he could opt to move away.
Smith's agent Stan Martin has previously said he and his client want to arrive at a decision before December 7, when the Storm are due to return to pre-season.