The new ward at RSH, which will open in the coming days, will increase the hospital's capacity by about 30 extra beds.
Simon Wright, chief executive at the Shrewsbury and Telford Hospital NHS Trust (SaTH), says the trust is asking for capital funding from NHS bosses in order to open a similar ward at PRH ahead of next winter.
It is expected to cost in the region of between £2 million and £2.5m.
Mr Wright said it would give the trust the capacity it needed while changes to hospital services take place under the Future Fit scheme.
He said: "We've built another ward on RSH. We will look to see if we can do the same thing on PRH next year."
Mr Wright said this winter was proving to be even busier for Shropshire's hospitals than last year.
He said the hospitals were seeing 33 patients a day more than expected, and 30 additional ambulances a day compared with the previous year.
Mr Wright said it had been 'tough so far', but thanked staff for their commitment.
"A huge thank you to the staff who are just remarkable," Mr Wright said. "They do a fantastic job."
He said improvements had been made at the trust since it was rated 'inadequate' by the Care Quality Commission (CQC) and placed in special measures last year.
Mr Wright said: "It's been very busy. We took immediate action when we received the letters and the concerns were raised with us."
He said assurances had been provided to the CQC every week since.
"We have been able to stabilise those services in a way we can all be a little bit more relieved about," he added.
He said the trust now has seven substantive A&E consultants, and the increase had been bolstered by the announcement of the £312 million in funding for Future Fit, which will separate planned and emergency care in the county.
The trust is also looking to recruit middle grade doctors from India, and has searched for staff in other areas of the world.
Mr Wright said he is confident the trust is providing a 'robust' service but that there is a need to secure more nurses.
He added that SaTH is also working to reassure international doctors and nurses at the trust over the uncertainties surrounding Brexit.
A report to SaTH's board, which meets on Thursday, says the trust has 214 EU colleagues, with the majority working in scheduled care.