Members of senior management will meet representatives from the NUJ, Bectu and Amicus tomorrow to talk about BBC director-general Mark Thompson's plans to axe 3,780 jobs.
It is understood that the talks will only take place if the BBC agrees to go into the discussions to negotiate.
Unions are hoping the BBC will look at other cost-saving tactics without the need for compulsory redundancies.
The impending 48-hour strike on May 31 is to be supported by up to 9,000 members of staff, including BBC presenters Natasha Kaplinsky, Jeremy Vine and Fiona Bruce who did not cross picket lines on Monday.
While some of the BBC's stars turned up for work, others like Radio 1 breakfast show host Chris Moyles and Radio 2 morning host Terry Wogan turned up as normal. Radio 4, however, did not air major programmes such as 'Today', because presenters including John Humphrys did not cross the picket.
Yesterday, the corporation played down figures from broadcasting unions, which hailed Monday's strike as the most successful in the BBC's history -- with between 13,000 and 15,000 staff staying at home.
The BBC claimed that 10,500 out of 17,000 expected to work had turned up and more than 90% of the corporation's marketing and human resources departments made it in.
Monday's strike caused a "mixed picture" across the channel with programmes such as 'Today' on Radio 4 and 'Newsnight' cancelled. The statement said at the time: "The BBC believes the best way forward is for unions to return to the table."
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