Many of the 36 staff affected by the plans are already looking for alternative work, said the council's craftsman gardener and GMB union senior shop steward, Kevin Chester. "The quality of parks will go down as a result of this," he added.
Chester, who has worked in the department for 26 years, saw Bedworth's Miners Welfare Park scoop the Best Public Park gong in 2000's Britain in Bloom.
He said: "We've got the pride of working for the council that we don't want to change. Morale in the department is at rock bottom."
The proposals affect £1.24m worth of grounds maintenance business. Drafting a specification for the contract is to begin in November this year, with a shortlist to be drawn up next February and the contract awarded in July.
Transfer of Undertaking Regulations (Protection of Employment) legislation means the department's 36 staff could be hired by an external contractor, but Chester said many are fearful for their jobs.
Former mayor, Councillor Bill Sheppard, agreed that an external contractor could mean future staff losses. "An external contractor will often offer much less favourable terms and conditions," he said.
The parks department is appealing to the Local Government Ombudsman and considering tendering for the contract itself. "We will be looking at going in at a lower price," said Chester.