The British Airlines Pilots Association will meet with bosses at Virgin Atlantic this afternoon for "last ditch talks" over working conditions.
BALPA said it hopes some headway can be made to "avoid confrontation between the airline and its pilots".
The union claims pilots are being denied their entitlement to 120 days off a year, in addition to holiday, in return for working over weekends and bank holidays.
Jim McAuslan, general secretary of the pilots union, said BALPA always does what it can to assist airlines through downturns.
"We did this with Virgin during these past difficult years. To now find that the company is breaching an agreement and denying many pilots their entitlement to the equivalent of a weekend off is a real slap in the face and one which we cannot accept."
A Virgin spokeswoman confirmed Virgin management would be attending a "routine, monthly" meeting with pilots.
The spokeswoman said Virgin would be "discussing any issues that arise, in that forum".
BALPA is rumoured to be preparing to ballot its members on industrial action, if the dispute cannot be resolved.
www.virgin-atlantic.com www.balpa.org