The measure would see public and private-sector workers stay away from work for 24 hours in protest at the Coalition's austerity programme.
If it goes ahead, it will be the biggest industrial action in the UK since the nine-day general strike of 1926.
The tactic, which would represent a significant escalation to the unions' protests against the coalition's austerity measures, will be discussed at the meeting of the Trades Union Congress's general council this month.
An internal document drawn up by Unite and seen by The Financial Times said it would be "desirable" to protest against Government cuts.
The document adds: "It would be a landmark in our movement's recovery of its morale, strength and capacity to play a leading part in a society crying out for credible and honourable leadership."
Unison, the biggest public-sector trade union with 1.3 million members, announced it also backed the principle of a general strike, although it stressed the move should be the culmination of a campaign against austerity measures.
The Public and Commercial Services Union, which represents nearly 300,000 civil servants, would also throw its weight behind 'co-ordinated action' aimed at the austerity measures.
GMB, the third biggest union, has not revealed its position on the proposed strike.
Conservative chairman Grant Shapps said that the Labour leadership should repudiate Unite after its plans for a general strike became clear.
"Labour's single biggest union paymaster is threatening British businesses and hard-working people with mass strikes,' he said.
"Ed Miliband must refuse to take a single penny more of his union paymaster's cash until Len McCluskey withdraws Unite's threat to sabotage our economy."
A spokesman for Labour, which derives up to 90% of its funding from union donations, said: "Strikes should be a last resort, and we are not in favour of a general strike."