A cabinet member has privately admitted that the introduction of is "highly unlikely" and would be political suicide for any administration.
The senior Labour group figure said the policy simply would not be introduced unless businesses in particular, as well as the travelling public gave their backing - and there is little, if any, support for it.
"I can't see it happening. The businesses will never agree to it and the councillors will not support such a move."
The spectre of workplace parking, a charge on free parking spaces provided by firms for staff, has been raised in discussion around
A report to the council's cabinet suggested such a move could raise £20 million a year to help pay for the new raft of Sprint bus and Metro lines.
Last week, council leader Sir Albert Bore said congestion charges and other transport taxes would only be considered if the business community could be persuaded of the case and once public transport improvements were in place.
The Greater Birmingham Chambers of Commerce has also expressed opposition to transport taxes, describing them as a "blunt instrument which will stifle economic growth".
Meanwhile, the Birmingham Connected plan was approved by the city's Labour cabinet.
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Opposition Conservative group leader Robert Alden broadly welcomed the 20-year vision for transport but raised concerns (CGIs below).
"I am disappointed to see that in terms of the tunnel closure we would go from four lanes to one," he said.
And warned that cycle lane improvements on Hagley Road, if delivered before new Metro or Sprint bus lines, would be "putting the cart before the horse" by reducing road capacity without the full range of viable alternatives.
"Some dual carriageways will be reduced to a single lane before the public transport is in place," he said.
Sir Albert Bore replied that the future of the tunnels would be looked at in detail and consulted on next year.