A new report reveals the shortfall of new homes needed in the Black Country is now 36,819, which has shot up from the 26,920 figure given two years ago.
And council planners say there are not enough brownfield sites in the region to cope with the growing population.
It comes amid campaigns to save areas like the Seven Cornfields in Wolverhampton from development.
Walsall Council boss Mike Bird expects the shortfall of homes to continue rising, saying the issue is now at "crisis point".
Councillor Bird said: "It will keep increasing because the housing shortage is such an issue, we are at crisis point. We have all got to look at the greenbelt and Walsall is no different.
"There is pressure on greenbelt, the whole of the Black Country. But our policy is brownfield first and we will continue to do that."
In Sandwell, there are less green spaces available to build on than other Black Country boroughs.
The council's deputy leader Maria Crompton said the Government is putting local authorities in difficult positions to meet housing demand, adding that urban areas may have to resort to building high rise properties as a last resort.
Councillor Crompton told the Express & Star: "The difficulty we have got is the Government is dictating how many houses we are supposed to provide.
"We have only got so much space. Most of the brownfield sites have either been built on or they are so contaminated that we cannot build on them.
"The Government are asking for something that we can't provide.
"We are in a bit of a dilemma. We are caught between a rock and a hard place. What do we do?
"We haven't got anywhere to build the houses, other than the small amount of green space that we have got. We don't want to do that but how do you get round it?
"We certainly don't want to start building high rise properties because that is not what people want.
"But it has got to be considered because we have got to look how best we can fulfil the Government's requirements."
The claims of housing shortages have come from a report published by The Black Country Plan – a joint planning project carried out by all four Black Country councils – Dudley, Sandwell, Walsall and Wolverhampton.
The latest report, called the Black Country Urban Capacity Review Update, said: "The review has found that the gap between supply and need over the new Black Country Plan period up to 2039 has grown to 36,819 homes, an increase of around 10,000 homes since 2019.
"Around half of this increase is as a result of a further loss of occupied employment allocations during 2020 in light of new evidence, and the remaining half is as a result of changes to the national housing method, which increased Wolverhampton’s local housing need by 35 per cent."
The next report on housing shortages is due next year.
But council bosses say the actual housing shortfall figures themselves are set by the Government.
And Dudley Council leader Patrick Harley expressed concern that the figures are inaccurate, branding them "utter nonsense", and he said he will be speaking with the Ministry of Housing, Communities and Local Government [MHCLG].
He told the Express & Star: "I think this uplift is arbitrary nonsense from MHCLG, I really do.
"It is utter nonsense to uplift by that capacity, utter nonsense. I certainly will be talking to our local members of parliament. We need to make sure our MPs are making it really clear to ministers of the impact of that decision.
"These are arbitrary figures which I don't believe are correct. We will certainly be writing to ministers to make our case. But these are absolutely arbitrary figures, they are nonsense."
Other councils and the West Midlands Mayor, Andy Street, all say they want to prioritise brownfield sites.
West Midlands Mayor Andy Street said he would work to help increase the number of brownfield sites being put forward for development.
Mr Street said: "There is still an incredible amount of derelict brownfield land left to develop, and I remain firmly of the belief that this is the answer to the Black Country’s immediate housing needs.
"I am committed to working with local councils to speed up the number of brownfield sites being brought forward, and we will continue to make Government cash available to clean up eyesore sites to pave the way for development.
"There remains pressure on greenbelt sites in and adjacent to the Black Country, but I will continue to give my full support to councils, communities and campaigners in resisting greenbelt development for years to come.”
Areas of land across the region have been put forward for development by landowners and developers. Among them is Foxcote Farm, Stourbridge, where 1,500 houses have been proposed.
Meanwhile thousands of people have signed a petition against 1,300 homes that could be built on 284 acres of farmland near Penn Common, an area known locally as the Seven Cornfields.
The proposed development would effectively fill the green buffer between Wolverhampton and Sedgley and remove open space enjoyed by tens of thousands living in the area.