The company, owned by private equity firm TPG Capital, has three branches in Shropshire.
It is set to launch a company voluntary arrangement, which will allow the Italian-themed chain to exit unprofitable branches and secure rent reductions on the remaining estate.
A total of 100 of Prezzo's 300 outlets have been earmarked for closure, as well as its Tex-Mex chain Chimichanga. It is not yet known which ones will close.
Prezzo has outlets in Oswestry, Telford, Bridgnorth and West Bromwich, while it also has a branch of its sister restaurant Chimichanga in Telford.
Prezzo, which is working with AlixPartners on the restructuring, employs 4,500 people.
The news comes at a bleak time for the high street and the casual dining sector in particular.
This year has also seen burger chain Byron and Jamie's Italian undertake CVAs as they come under increasing pressure from rising costs and falling consumer confidence.
As well as staff costs and lower footfall, the chains have been stung by the collapse in the pound, which has ramped up the cost of buying ingredients.
Soaring business rates, National Living Wage costs and the Apprenticeship Levy have also taken their toll.