The council is expects to let a three-year contract, but is is also looking at a variant bid of five years plus an option to extend by two years taking the expected value to around £238m over the seven year term.
A bidders day to set out terms for prequalification is planned for 10 May.
Expressions of interest are to be registered via YORtender ref: YORE-96MK95, closing date 5 June.