The public consultation focuses on three proposed extensions to the network, which aims to improve access to open spaces and create a series of 'green' travel corridors across the borough.
During 2020, the council repaired and laid more than 2,000 metres of pathways at New Bilton's Freemantle Open Space and Brownsover's Sorrel Drive and Brooklime Drive.
The wide paths allow visitors to avoid areas of open spaces prone to becoming boggy during wet weather while protecting wildlife habitats.
Now the council has drawn up plans expand the network - with a 'west' route linking Apple Grove, Cornwallis Open Space, Freemantle play area, recreation ground and open space, and Addison Road Recreation Ground.
A proposed 'east' route aims to create a pathway network between GEC Recreation Ground and Lower Hillmorton Road to Lansdowne Place and Fleet Crescent, Whinfield Recreation Ground, Whinfield Wood and Whinfield Cemetery.
In addition, the east route includes plans for pathways between Linnell Road Open Space, Wise Grove, Bluebell Walk and The Kent.
Finally, a proposed route in Brownsover includes improvements to pathways which link the Warwickshire County Council cycle path between Boughton Road and Crowthorns to the path near Helmdon Close, and improve links to the Staveley Way area.
The council also hopes to install eco-friendly, solar-powered lights on the proposed routes.
Residents can take part in the public consultation by visiting the council's website: www.rugby.gov.uk/parkconnector
The consultation supports the council's applications for funding to deliver the plans.
Cllr Howard Roberts, Rugby Borough Council portfolio holder for environment and public realm, said: "The feedback we've received from residents about our work on the Park Connector Network has been extremely positive, and we're keen to extend the network to other parts of the borough.
"Feedback from residents plays an important role in securing funding for such projects, so I'd encourage residents to take part in the consultation and have a say on our plans."
The consultation closes at 5pm on Wednesday 31 March.