The former Warriors captain and Dally M medallist's rugby union career is in limbo after missing selection for the All Blacks last weekend, but Webster told media on Tuesday that Tuivasa-Sheck is not in his immediate plans.
"Mate honestly, I have not mentioned that to anyone. No one has mentioned that to me ... we have certainly not spoken to Roger about that," he said.
"I don't know if there's room in the cap. We're happy where we're at as far as what we want to do this weekend, so that's what we're focusing on ... he looks very solid and fit, but I don't know how that would relate.
I'm thinking about Roger for next year, I'm not thinking about Roger for now. I just want Roger to be happy for the rest of the year, if he's happy, I'm happy."
Rumours have also swirled that Tuivasa-Sheck may be signed to a short-term deal to his other former club, the Sydney Roosters, for the remainder of the 2023 season.
Meanwhile, you could be forgiven for thinking that the bye week has pinched a bit of momentum from the sixth-placed Warriors after their impressive back-to-back wins over the Dolphins and Canberra. However, Webster says that the break has left them refreshed.
"We've got a clear focus of what's coming," he said.
"It's given us time to practice and fix things that you don't get time for on a six day turn around. You don't want to fiddle with things on a short turn around because you just don't have enough time."
Webster welcomes back half Dylan Walker for their game against the struggling St George Illawarra. The former NSW Origin rep has undergone a form revival after shifting to Auckland this season, before succumbing to a toe injury that kept him sidelined for the last two games.
The Warriors will be looking to exploit a Dragons side in turmoil, after revelations this week that captain Ben Hunt is willing to reach into his own pocket to affect an immediate release from the 15th-placed club.
Webster says that the events haven't reflected what sort of a threat the Dragons are, and that Hunt has been playing "unbelievable football".
"Where you look at them on the table doesn't matter right now," Webster said.
"They've beaten some good teams lately, they're at home on their patch of grass. We've got a lot of work to do."
A win in Wollongong will lift the Warriors to a share of fourth place on a very congested NRL ladder, with only six points separating leaders Brisbane with the 11th-placed Roosters.
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