The 7,000 workers of the UK’s largest car manufacturing plant survived a cost-cutting decision last week.
Mr Frost was answering questions from Peers on the House of Lords EU Committee
The bloc’s chief negotiator said it had always remained open to any extension.
Ministers will launch a fresh attempt to repeal EU freedom of movement in the UK as flagship immigration legislation appears before MPs.
The EU’s chief negotiator Michel Barnier warned the ‘clock was ticking’.
Both sides "took stock of the technical work" that had taken place since the last negotiating round, and looked ahead to further talks.
Of the money spent, £1.9 billion went on staffing costs.
The proposed day off would fall close to June 23.
The government predicts a deal could boost US-UK trade by £15.3 billion.
The Prime Minister’s trade negotiator David Frost is due in Brussels for the first round of post-Brexit discussions.