Bectu, Amicus and the National Union of Journalists met Thompson for a three-hour meeting yesterday to try to resolve the dispute and prevent industrial action.
A strike ballot was seen by the unions as unavoidable because, they said, Thompson was not prepared to delay the proposed 3,750 job cuts to allow an "in-depth discussion" about the future of the BBC.
Thompson did promise that no redundancies will be made until June, but could not guarantee that all the job cuts would be voluntary.
Luke Crawley, Bectu's chief BBC official, said: "These are the most damaging cuts in the BBC's history, with nearly one fifth of all staff being made redundant, and thousands more due to be handed to new employers."
Notice of the strike ballot is due to be sent to BBC management today, with voting papers to be sent out to staff next Wednesday.
If union members vote for strike action it could lead to major disruption of BBC programming and affect its coverage of the May 5 General Election.
In response the BBC said that it had every intention of working with unions to address staff concerns, but was not able to rule out compulsory redundancies.
The BBC said that it had outlined to unions the challenges that it faced and argued that the three year plan of efficiencies, savings and different ways of working would mean the corporation could put an extra £355m a year into programmes from 2008.
"The BBC believes it is a matter of real regret that the union representatives have chosen not to continue with what we believe could have been a constructive and meaningful dialogue, as we believe our staff want early clarity on what the change plans mean for them.
"We regret the unions' decision to ballot their members for industrial action," the BBC said in a statement.
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