It builds on work already undertaken by the local authority on tackling trade waste.
CLA president Harry Cotterell said: "It costs around £800 to deal with each incidence of non-toxic fly-tipped waste on private land.
"Although we would like to see waste taken to local tips free of charge, we understand this is unlikely without a change in the law.
"However, the partnership with Suffolk County Council should help identify the barriers preventing fly-tipping from being dealt with.
"There must be a long-term sustainable solution, so we are pleased Defra is seeking to provide funding for the joint effort and, if successful, the outcome could be rolled out to other local authorities."
One idea the CLA is keen to explore is a ticketing scheme for victims that uses a reference number to trace the crime, from the point of reporting the fly-tipping to the police or local authority to disposing of it at the local tip.
Mr Cotterell added: "The CLA will also continue to lobby the government to remove the potential for landowners to be prosecuted purely because they have not removed waste tipped on their land."
The partnership was announced at a recent government summit on fly-tipping, chaired by Defra minster Lord Taylor of Holbeach.
The summit was a key government commitment to bring organisations across all sectors together to galvanise support for regional action on fly-tipping.