Swinney told the Scottish Parliament at Holyrood: "The company [Vion] will continue dialogue with any interested buyers.
"As I understand it, there has been a further expression of interest in Hall's in recent days.
Groups of bidders
"I have already met one of the groups of bidders personally in my office and my officials have spoken with two others, making three interested parties at this stage.
"The government is only too prepared to advance dialogue with those parties to find if there is a way we can maintain employment at the Hall's of Broxburn site."
The new hope of saving the jobs emerged after Vion last week rejected an offer by the Scottish government to buy and lease back the site.
A spokesman for the Dutch based multi-national meat firm said: “We greatly appreciate the serious offer of support the Scottish government has made and thank them for the significant assistance they have provided since the start of the consultation process.
“However, given the scale of the losses at Hall’s of £79,000 per day, and the complexity and inefficient layout of the factory, we regret that we are unable to accept this support.
‘Wrong to accept public money’
“It would be wrong to accept the offer of public money knowing it is significantly below the amount required to resolve the core legacy problems at the site. It would serve only to delay any potential decision regarding closure.”
Swinney said staff at the threatened plant would be supported with counselling. Officials from Skills Development Scotland and Jobcentre Plus have visited the site to offer support.
Vion’s consultation on its plans to close the meat plant The consultation ends in two weeks.
Meanwhile, a reader contacted FoodManufacture.co.uk to warn that far more than just the 1,700 jobs at the meat plant were at risk.
The reader – named Sarah – said: “There is a lot more behind this story, other than the 1700 jobs. Producers, haulage staff, vets, quality assurance are all on edge.
“There is a piggery industry holding on to the hope that livelihoods are going to be saved as well. Many Scottish producers cannot afford to haul their livestock to the Vion plant in Malton, as with the increasing grain price this year, we are already struggling to produce a pig that makes money.
"I speak from experience and know that this will result in a large number of unemployed farm workers as well as pig sheds, if this isn't resolved.”
To read more about Vion’s rejection of the Scottish government rescue plan, click here.