The postal firm Consignia - which is seeking to outsource parts of its business to help cut costs - said Securicor had been chosen as its preferred supplier of cash services.
About 3,000 workers are currently employed by Consignia in its cash-handling operations, and a number of these will be transferred to Securicor if the deal goes ahead.
But the Communication Workers Union (CWU) said the government should step in to stop the move, describing it as "blatant privatisation".
"If they (the Consignia workers) wanted to work for a private company they could have chosen to do that, but they haven't," said CWU assistant secretary Andy Furey.
"It's disgraceful that Consignia is playing musical chairs with their jobs. When the music stops who knows where they'll end up."
Consignia said detailed contract talks with Securicor were now under way and "discussions continue with the unions to get the best possible arrangements for employees."
Cashing-in
In addition to servicing the UK's post offices the contract also covers cash deliveries to about 2,000 other organisations.
Consignia currently operates 40 cash-in-transit depots in the UK and uses a fleet of 700 vehicles to move the cash.
It also has 20 cash centres where the money is counted, processed and stored.
Securicor said that if it won the contract it would carry out about 1.6 million cash transportation services each year, involving £37bn in notes and £2bn in coins.
Consignia is currently undergoing a major restructuring aimed at stemming huge losses.
A total of 17,000 jobs are to go as part of the shake-up, and Consignia's name will change to Royal Mail Group at the end of the year.