Workers at Chivas Brothers were told yesterday that the company planned to sell the plant to the Benriach Distillery Company.
The workforce at Newbridge will be slashed from 103 to just 24.
Chivas is offering the chance for up to 60 workers to transfer to its other sites at Paisley and Dumbarton.
Chivas – whose brands include Chivas Regal, Glenlivet, Ballantine's and Beefeater gin – is owned by Pernod Ricard, whose executives were said to have been "shocked" at the attitude of First Minister Alex Salmond when he met them in Paris last month.
Mr Salmond was reported to have been "aggressive", "extremely rude" and "unwilling to listen to reason" during discussions about minimum pricing for alcohol.
But the company said the Newbridge announcement was not connected in any way with Mr Salmond or minimum pricing.
A statement said: "If the sale proceeds, 24 employees will have the opportunity to remain at Newbridge and 60 will be offered alternative jobs at our other sites.
"We hope that many employees will take the opportunity to transfer so that the impact on employment is minimal.
"If they choose not to move, a generous redundancy package will be made available to them."
The proposed sale is due to take effect in July next year.
The statement said the move would "maximise manufacturing efficiencies by fully utilising capacity at our larger sites".
It added: "We remain committed to the long-term growth and development of Scottish whisky and we will continue to invest in our brands and our business."
Lothians Labour MSP George Foulkes said he would be raising his concerns with finance secretary John Swinney.
He said: "I will be pushing him to do everything he can to make sure there is individual help for the workers in terms of retraining or finding alternative employment."
SNP Lothians MSP Shirley-Anne Somerville said: "It is always disappointing to hear of jobs being lost to the Lothians. I have been in contact with Chivas Brothers and will continue to work with them to ensure that any employees taking redundancy are given the best possible support."
A Scottish Government spokesman said Mr Swinney spoke to the company yesterday.
The spokesman said: "The Scottish Government will offer support though Partnership Action for Continuing Employment to provide tailored help for any staff that face redundancy."