The new A-League club has already announced Panagiotis Kone, Josh Risdon, Connor Chapman and Aaron Calver as their first signings.
John Anastasiadis and John Hutchinson have been appointed as the franchise’s assistant coaches.
But The World Game understands United are keen to lure forward Williams and goalkeeper Kurto across the Tasman.
The Victorian club’s new head coach, believed to be Phoenix boss Mark Rudan, wants to bring the duo with him.
Williams is off-contract at the end of this season, after signing a one-year deal when he left Haladas, and as a free agent would be free to join Western United.
The well-travelled former Socceroo, who has played in Denmark and Hungary, has recaptured his best form under the coaching of Rudan in New Zealand in the past six months.
Williams has started all but one of Wellington’s A-League games this season.
The 31-year-old, who can play up front or one either wings, has banged in seven goals from 20 appearances for the much-improved Phoenix, and has two caps for the Socceroos.
Polish keeper Kurto joined Wellington on a one-year contract from Dutch outfit Roda JC Kerkrade in July last year, and is also set to leave the Phoenix at the end of the 2018-19 campaign.
The 27-year-old, who has represented his country at junior international level, has impressed in New Zealand.
Kurto has made 19 appearances in the A-League, notching five clean sheets.
The shot-stopper leads the competition for saves with 78. Central Coast Mariners keeper Ben Kennedy is second with 70.
Earlier this month, reports linked Kurto with interest from European clubs.
“I really enjoy it here. The level of the league and the team, it's very good. [Wellington] is really good, it's really calm which is what I like.” Kurto told reporters.
Rudan has declined to commit to Wellington for next season, despite having a year left on his contract with the club.
The 43-year-old has also said publicly he won’t be with the Phoenix next year unless his Sydney-based family relocates to New Zealand.
"My family is the big one," Rudan told Radio Sport.
"They are first and foremost. I have struggled to live without them. We have had discussion about it, but I've made a decision that my family has to be with me.
“It's not going to be a come and go situation. It just doesn't work. My boys need me, I need them as well. The club are working hard to try and improve the situation."
