The contract, currently held by English Landscapes, covers five main parks, three of which are Green Flag-accredited.
According to the borough's parks manager Mel Henley, a key aim of the contract will be to secure more awards. "We are hoping to improve on our three Green Flags," he explained.
The deal, which could be extended by five years, is split into eight lots. Contractors will be able to tender for the whole package of grounds maintenance works and for individual lots, added Henley.
"We are expecting contractors to price the whole as a package and as individual lots, which will leave the council the opportunity to either take the entire package or to split it up to get the best result," he said.
Among the parks in the contract are grade II-listed Dunorlan Park, popular site the Grove and Woodbury Park Cemetery.
Work also includes the maintenance of sporting facilities from county-standard cricket pitches to bowling greens and assistance in managing the area's Cricket Week in late May or early June. Tree work is also among the lots offered, as well as play equipment inspection and maintenance. The deadline for applications is 12 March.
For more information, email Mel Henley at firstname.lastname@example.org or call 01892 526121.