Chancellor George Osborne announced potential bidders should respond by the end of the month, saying the aim was to maximise value for money for the taxpayer.
The decision was attacked by rail unions, while Labour warned it could follow the Royal Mail privatisation as a “rushed and under-valued” sell-off.
The Government announced last year it wanted to achieve £20bn from corporate and financial asset sales by 2020. Subject to achieving value for money, the Government said it expected to reach definitive agreements in the first quarter of 2015
Since services began in 1994, Eurostar has carried over 145 million passengers, with over 10 million in 2013 alone, while sustaining traffic growth every year for the last decade.
Mr Osborne said: “I am determined that we go on making the decisions to reform the British economy and tackle our debts.”
The French state train company SNCF owns 55 per cent of Eurostar and Belgium’s SNCB holds 5 per cent.