Alainu'uese remains under contract with the Warriors at least until his current deal expires at the end of this season but head coach Dave Rennie wouldn't rule out the possibility that the big lock forward could leave for the French club in mid-season.
Rennie says Warriors want to see Alainu'uese back from injury and getting a run of games before making a new contract offer.
Speaking in The Courier ahead of Glasgow's PRO14 match against Southern Kings in Port Elizabeth, Rennie said: "Brian's been injured pretty much for a big chunk of 14 months.
We've spoken to him and said we're unsure whether we'll re-sign him, he'd need to come back and play a big string (of games) to convince us we'd get our worth out of him.
"Players are constantly trying to get clarity around their future, so they're looking at opportunities elsewhere. For Brian, that could be with us or with Toulon, but there's nothing concrete."
Reports from France claim Toulon are keen to bring Alainu'uese in mid-season.
"I'm not saying that's impossible," said Rennie. "If someone came in and made a commitment to Brian beyond this year, we'd look at it.
"What we've said to him is we want you to stay with us but we're not going to offer you anything yet. Transfer fees can happen, but we want what's best for us and best for Brian.
"Really, we just want to get him back on the field playing. We can't commit to him and a number of other guys until we get them on the park and see them playing.
"Some guys may not be prepared to wait that long, because it's their future and they want to have a plan for next year. Brian's in that situation."