Fa'asuamaleaui has a clause in his contract that allows him to speak to other clubs from November 1 for the 2027 season.
Titans chairman Dennis Watt has told AAP the club is determined to keep the inspirational Test and Queensland prop.
The 25-year-old's manager Simon Mammino told AAP that ideally he wants to stay at the Titans and help take the club to a premiership, but the uncertainty over the coaching future of Des Hasler and overall club direction has led to him deciding to explore other options.
Perth Bears coach Mal Meninga, formerly the Titans' head of performance and culture, was a major factor in the 2020 premiership winner joining the club from Melbourne in 2021.
Former Titans recruitment boss Ezra Howe, now in the same role at Perth, was also influential.
"We will have a look around (on November 1), but that's because we don't really know what's going on at the club at the moment," Mammino said.
"Tino would probably prefer to stay. We just want to see some decisions made that the club is stable."He has got time to make a decision, so hopefully they will resolve where the club is at with the coaching situation for 2027.
"That's not to say he doesn't want Des there. He gets on well with Des. It's also about where the club is heading with the re-signing of a couple of players."It gives us time to look at what the club is doing. I have got confidence in the chairman Dennis Watt, (CEO) Steve Mitchell and the owner Rebecca Frizelle.
"It's just a recheck clause that we put in there to see where the club is at and where he is at and what options are there to consider."
Watt said the Titans had stability on the coaching front and wanted Fa'asuamaleaui to stay.
"The owners put out a statement recently saying Des is here for 2026," Watt told AAP.
"Tino is very much part of our future plans. He is an inspiring leader and we want to keep him here."
Fa'asuamaleaui's parents live in Gympie and his in-laws live on the Gold Coast, so he is settled off-field, but the Meninga factor at Perth has them in prime position to make him an offer for their 2027 entry.
"With Perth it is about being part of a new franchise that has history with the North Sydney Bears, which is attractive to any player," Mammino said."Mal being part of a new franchise is attractive like it was to players going to the Dolphins (under Wayne Bennett).
"It's not all about money, but at some stage in the off-season we will speak to Perth, who will have a full salary cap to spend. The Dolphins targeted Tino, but he stayed at the Titans after (former coach) Justin Holbrook was sacked."
Meninga was previously a magnet for Fa'asuamaleaui.
"Mal and Ezra are the two that got him there to the Titans," Mammino said.
"Mal was the Australian coach and has a fair aura about him. He was there to improve the culture at the Titans, and the words Mal had with Tino and his family gave him confidence the club was rebuilding and heading in the right direction.
"Tino was a key figure in that and was confident to go to the Titans with Mal there."
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