Austrian Wolff bought into Williams in 2009, but over the winter he also became a co-owner of F1 rival Mercedes.
Apr.15 (GMM) Williams will survive if Toto Wolff withdraws his major stake in the famous British team.
That is the vow of Claire Williams, who is founder and boss Sir Frank Williams' daughter and the new deputy principal of the Grove based team.
Because of his new management role, Wolff no longer works at Williams, but he has vowed to end the 'conflict of interest' by finding a buyer for his team stake.
He has pledged to do it responsibly.
"I cannot just go into the market and say 'who wants to buy these (Williams) shares' and that's it," he told Reuters.
"If I sell, I have to find somebody who is responsible enough, who is coming in for the sport, who understands how the team functions, hopefully a sponsor," added Wolff.
"And this is not so easy to find somebody who is suitable."
Time could therefore be on Williams' side, but Claire Williams insists that - no matter what ultimately happens - the health of the team is not at risk.
"Toto is a big shareholder and he's a great shareholder," she said.
"If he feels there's conflict then he has to make the decision in the best interests of his position and we would respect that. But we'll wait and see what happens.
"We are doing a good job on the commercial front," Claire Williams added.
"We are financially stable and have a good healthy budget to go racing with. We're not complaining about that and there aren't concerns that we aren't going to be here next year."
Wolff's wife Susie is a Williams test driver.