The 61-year-old is thought to feel he has taken the side as far as he can after the 1-0 loss in Montenegro to open the 2012 Euro qualifying campaign.
He may leave before next month's games against Bulgaria and Switzerland, but would stay if needed for those matches.
Toshack, whose second period in charge of Wales began when he succeeded Mark Hughes in November 2004, has won 21 and lost 24 of his 53 games since then.
The former Real Madrid manager is not thought to be under any pressure to step down from Football Association of Wales chiefs, but he was seen in deep discussions with high-ranking officials after the disappointing defeat in Podgorica.
FAW vice-president Trefor Lloyd Hughes told BBC Wales that Toshack was extremely disappointed after Wales' loss in Montenegro and that further news could be expected this week.
"There's a lot of speculation, some of it false, some of it true," said Lloyd Hughes. "The FAW, I'm sure, will issue a statement clarifying the situation either later [Monday] or by midweek."
Immediately after the loss to Montenegro, former Wales internationals Iwan Roberts and Robbie Savage called for Toshack to go.
"Our optimism is gone in one game, I don't think there were any positives," Roberts told BBC Radio Wales' The Back Page programme.
"Toshack has taken the squad as far as he can. He's been with them since November [2004] and have we progressed? I'm not too sure.
"I would say his position is untenable if we lose to Bulgaria, we have to get six points from the next two games."
Savage, an old adversary of the Wales boss, told BBC Radio Five Live: "It is time John Toshack left Wales.
"I think we need a fresh start, fresh impetus. We need to get the crowds back and I think Toshack has to go.
"He has made enough excuses, he has been in the job six years. Judge him on his qualifying campaigns - they haven't qualified yet and they have got off to a terrible start again."
Former Wales midfielder Mickey Thomas was more restrained, but also saw the Bulgaria match as a watershed.
"I'm not sure it's right or helpful to call for the manager's head after one game," Thomas told BBC Wales.
"But if Bulgaria doesn't go well then the pressure mounts and maybe his time is up.
"Only two men could change things around quickly - Ryan Giggs and [Wales Under-21 manager] Brian Flynn, that combination could get the Welsh team going."
After a glittering playing career with Liverpool, Toshack became player-manager for fourth-division side Swansea and by 1979 had guided them to the old first division.
After that, Cardiff-born Toshack coached Real Madrid, Real Sociedad and Deportivo La Coruna in Spain, Turkish side Besiktas, French club St Etienne, Portuguese outfit Sporting Lisbon and Catania of Italy.
He walked out on Wales in 1994 after just one game in charge when he realised the extent of support that existed for the man he had replaced, Terry Yorath.
When Toshack took the national job again 10 years later on a five year-deal, Toshack warned it would take longer than that to rebuild the team, and he signed a two-year extension in 2009.
He suffered a host of high-profile international retirements such as Gary Speed, Mark Pembridge and Andy Melville before John Hartson, Mark Delaney and Ryan Giggs stepped down from Wales duty.
But he has overseen the development of highly rated Wales youngsters like Gareth Bale, Aaron Ramsey, Wayne Hennessey, Joe Ledley, Ched Evans and Jack Collison.
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