The airline, Asia's largest by revenue, needs the agreement of two-thirds of its roughly 16,000 employees and 9,000 retirees for the cuts so it can reduce a pension shortfall estimated at 331 billion yen ($3.6 billion) at the end of March.
JAL has won the support of current employees for a halving of payouts and is asking retired workers to accept by Tuesday a cut of around 30 percent.
But as of Monday only about half of retirees had agreed to the plan, the Nikkei Business daily said.
JAL plans to extend its efforts to convince retirees to January 22 if it cannot get their support by the Tuesday deadline, media said.
A JAL spokesman said he did not have an update on how many retirees have agreed but added the firm would continue its efforts to persuade them beyond the deadline if it fails to secure consent by Tuesday.
JAL, weighed down by $16 billion in debt and mired in losses, applied in late October to the Enterprise Turnaround Initiative Corp of Japan (ETIC), a body of restructuring specialists that can tap state-backed funding to bail out ailing companies.
The ETIC plans to inject about 300 billion yen in fresh capital into JAL, provided it file for bankruptcy and creditors agree to waive around 350 billion yen in debts, sources told Reuters last week.
The ETIC is eyeing some time between January 19 and January 22 for the carrier to file for bankruptcy and for the ETIC to officially announce its plans to offer its support.
The ETIC plans to have JAL's pension fund dissolved if JAL is unable to get support for the cuts on its own, likely triggering even larger cuts for employees and retirees, a source with knowledge of the matter has said.
(Reporting by Nathan Layne and Taiga Uranaka; Editing by Rodney Joyce)