The county town has lost out in two previous civic awards competitions, but the council says no bid will be drawn up this time around due to resources being focussed on the pandemic.
New cities were last created to mark the Diamond Jubilee in 2012, with St Asaph, Chelmsford and Perth winning the honour out of 26 entrants, while Armagh was awarded a Lord Mayoralty.
Shropshire Council leader Lezley Picton said: “The issue of city status has been looked at numerous times before.
“Given the current focus on post Covid-19 recovery we have decided that our resources are best concentrated on economic and social recovery and delivering important local services.
“We simply do not have the capacity or finances to spend time bidding.”
Shrewsbury first bid for city status in 2000 when a contest was launched to mark the turn of the millennium, but lost out to Wolverhampton, Inverness and Brighton and Hove.
A second attempt was made in the 2002 competition to mark the Golden Jubilee, but Shrewsbury was once again overlooked in favour of Preston, Newport, Stirling, Lisburn and Newry.
Towns including Telford, Newtown, Machynlleth and Wrexham were also unsuccessful in both rounds.
No towns in Shropshire or Powys bid for the honour in 2012, but Wrexham lost out again as did Dudley in the West Midlands – and both have announced they will be throwing their hats into the ring again next year.
They will be up against the likes of Reading, Milton Keynes, Boston, Medway and Swindon.
A separate contest is also open for current cities to apply for Lord Mayor or Provost status.
Councils have until December 8 to submit their bids.
Chloe Smith MP, the constitution and devolution minister, has said entries are encouraged from “vibrant towns and cities with distinct identities, history, and sense of community”.