Once complete, the strategic outline case will be submitted to NHS bosses for formal approval, but parts of the major scheme could also be hurried along to address "immediate operational issues".
The plans have been years in the making and a progress update will be given to the board of directors at Shrewsbury and Telford Hospital NHS Trust during a meeting on Thursday.
A report to the board says the trust undertook a a procurement exercise last month to appoint a preferred supplier for the work.
Under the scheme, which has been renamed the 'hospitals transformation programme', Royal Shrewsbury Hospital will house the county's main A&E, with Princess Royal Hospital in Telford due to get an 'A&E Local'.
PRH will also take over responsibility for planned care but is due to lose its consultant-led women and children's services.
However, the report also acknowledges the challenges ahead as the funding requirements for the project have risen to more than £530 million, mainly due to increases in inflation rates.
That figure is much higher than the £312m approved by the Department of Health and Social Care three years ago.
The report says opportunities to accelerate the implementation of the scheme are being explored, with the aim of "delivering a proportion of the benefits in advance of the main infrastructure development".
It says: "Two business cases have been developed to increase capacity across Shrewsbury and Telford hospital sites.
"These two business cases, if approved, will allow the trust to establish additional ward capacity at RSH and enable elective inpatient and day case capacity to be protected at both RSH and PRH; address capacity and quality issues in respect of renal medicine at PRH through the transfer of the service into a dedicated community unit and provide capacity flexibility to support the first stages of service reconfiguration.
"The trust is planning to develop further business cases in the coming months, for implementation over the next four years, which will support the acceleration of acute reconfiguration benefit delivery."
Health bosses say the Future Fit scheme will improve patient care and help reduce cancellations of planned procedures.
But it has been met with widespread opposition.
The plans were reviewed under the instruction of Health Secretary Matt Hancock in 2019, following a request from Telford & Wrekin Council, after being confirmed by the local clinical commissioning groups in January of that year.
Scores of protestors turned up to the Future Fit decision-making meeting at Harper Adams University, near Newport, with some holding up banners which said the county should keep both its A&Es.
The report adds: "The trust is presently working to complete an updated strategic outline case (SOC) by the end of July, which will then be submitted to NHS England/Improvement for formal approval.
"The finalised SOC will be available for wider circulation following approval by NHSEI."