Private investors are being sought to fund the building of a new 200-bedroom hotel, with one site under consideration being The Quarry Swimming and Fitness Centre, which would be demolished to make way for the hotel.
It had been hoped the plans would include provision for a new leisure centre to be built elsewhere in the town centre.
But council bosses said today there are no public funds available for such a move.
Even if the hotel idea does not come to fruition, the council said the ageing leisure centre is "coming to the end of its natural life". But they said there are no "current plans" to close the centre.
They said the current financial climate means there is no money available for a replacement, despite the scheme being identified by the former Shrewsbury & Atcham Borough Council as one in need of funding before it was replaced by Shropshire Council in 2009.
Councillor Gwilym Butler, Shropshire Council's Cabinet member for leisure, said: "The Quarry swimming and fitness centre is coming to the end of its life and its replacement is something that has long been aspired to by both the former Shrewsbury & Atcham Borough Council (SABC) and Shropshire Council, subject to funding being available.
"However, it's important to make clear that no money was set aside by SABC for the replacement of the swimming centre."
He added: "Shropshire Council wants to provide people with the best possible swimming and leisure facilities. Unfortunately in the current financial climate there is no money available at the moment for the replacement of the swimming centre in Shrewsbury, and we have no current plans to close the centre."
Councillor Steve Charmley, Shropshire Council's cabinet member for business growth, has previously said it is estimated the hotel would cost £40 million to develop and build. He said: "A number of possible sites in or close to the town have been identified, including the Quarry Pool site, and we are keen to talk to hotel operators and leisure developers about the options."