Lycett comes out of contract at the end of this year and the South Australian has the option of returning home to link up with Port Adelaide, who are in desperate need of some ruck support for Matthew Lobbe.
Hurn also hails from South Australia, but has been happily nestled in Perth since being drafted by West Coast with pick No.13 in the 2005 NAB AFL Draft.
With Eagles great Dean Cox retiring at the end of the season, Lycett is expected to re-sign with West Coast for a further three years.
Lycett booted a career-high four goals in Sunday's 60-point win over Collingwood, and Hurn hopes the 21-year-old will stay an Eagle beyond this season.
"I think he will," Hurn said on Monday.
"It's one of those things that as a player you never want to intrude on an individual's preference on what he wants to do.
"But we certainly encourage players to stay."
The Eagles are also rumoured to be closing in on a new deal for Jack Darling, whose current contract runs out at the end of next year.
Hurn will notch his 150-game milestone in Saturday's crunch clash with Essendon at Etihad Stadium.
The 26-year-old said he never seriously considered leaving West Coast despite his strong family ties in the Barossa Valley.
"WA is a nice spot with nice weather," Hurn said.
"I have a few good mates here now and I didn't want to move.
"I consider myself half West Australian now; half SA boy. It's great. I'm really proud."
Hurn has been a key driver in West Coast's recent revival, with his rebound from defence proving crucial in wins over Adelaide and Collingwood.
The Eagles sit just one win adrift of seventh spot and Hurn said it was pivotal for the team to keep their momentum going ahead of Saturday's crunch clash with eighth-placed Essendon at Etihad Stadium.
Hurn is expected to be handed the captaincy for his milestone match, and the booming right-footer said it would be nice to land the role full-time next year.
Matt Priddis, Scott Selwood, Josh Kennedy and Eric Mackenzie are other players in the running.
"It would be something great to do because it's such a great club," Hurn said.
"But we've got five or six other players that could do it as well."
