Shropshire Council's cabinet will consider the plans, which would be for five years, at its meeting next Wednesday, July 6.
The site would be close to the north east corner of Ellesmere Road roundabout, between the A5124 Battlefield Link Road and the A528 Shrewsbury Road.
It is owned by Shropshire Council and the authority said it would be screened by "a belt of trees".
The move follows a two-month public consultation into the plans in autumn 2020, with the proposal then delayed by the pandemic.
The council said the site, which is intended to tackle the problem of unauthorised encampments in and around Shrewsbury, would provide a safe place for families to stay while passing through the county.
The site would accommodate up to eight families for short periods of time, not exceeding three weeks at any one time.
Subject to cabinet approval, a planning application will be submitted, with the site expected to open within 12 months.
The authority said that the consultation generated 55 responses of "mixed" opinion, though the aim to reduce unauthorised camps was "widely supported".
The council said that a transit site within Shropshire is being proposed for several reasons.
A spokesman for the authority said: "There’s a need for a safe place for gypsy and traveller families to stay whilst passing through the county.
"The site will also resolve a short-term problem for gypsy and traveller families who are due to move onto the council’s owned and managed sites.
"Secondly, national planning policy for gypsy and traveller sites requires local authorities to identify and to seek to meet the permanent and transit accommodation needs of gypsies and travellers via the planning process.
"Lastly, though the police have powers to evict unauthorised campers, these are discretionary."
Dean Carroll, Shropshire Council’s cabinet member for physical infrastructure, said: “In recent years we’ve seen a number of unauthorised encampments in and around Shrewsbury and a significant number pitching on high profile locations such as the park and ride sites, Battlefield Enterprise Park and the retail business car parks, impacting both on the public and private sectors.
“Some areas within Shrewsbury experience regular unauthorised encampments, which can cause disruption and conflict locally, and can also be expensive and time-consuming to clear. And we cannot evict unauthorised camps if we have no provision to move them to.
“Such a transit site could, within a reasonably short timescale, deal with the ongoing and costly issues associated with such encampments and help ease the impact on local communities and businesses whilst longer term site provision is considered.
“We anticipate that the site will also have a positive impact on gypsies and travellers, and on community relations between traveller and settled communities.”
The council said the proposed site would be of "basic construction", with a stone or grasscrete base, portable toilet block units, which will be removed during no-occupation periods to prevent vandalism, CCTV, perimeter fencing and height restriction barriers on the entrance to the site.