Royal Mail has owned the contract to collect, screen and deliver MSPs' mail since the Scottish Parliament opened.
But the contract has come up for renewal and has to go out to tender because of competition laws.
Postal workers' representatives said they were worried that the contract will be awarded to Business Post, a private company based in Slough.
"
It would be very ironic for them to opt for a private internal mail system
"
Derek Durkin, CWU
They fear 12 staff and their manager will lose their jobs.
The Communication Workers Union (CWU) said it would be hypocritical for MSPs to defend rural postal services but allow their internal mail to be privatised.
CWU spokesman Derek Durkin said: "All political parties in the Scottish Parliament support a publicly owned postal sytem.
"So it would be very ironic for them to opt for a private internal mail system and we would obviously arch against that."
A parliament spokeswoman said the contract is still under negotiation and that no decision is expected until the end of April at the earliest.