The offer, reviewed by Reuters, comes after weeks of negotiations between the company and union following a two-day strike in July. Telmex followed up with a proposal in August, but both sides decided to continue talks.

The new proposal says workers who join the company after Oct. 1 will receive, upon retirement, an annual December bonus equivalent to 10 days of pay, as well as a 10-day bonus in August.

The proposal document did not specify whether the August bonus would also be annual, or include further details about the pay-out of the perks.

Telmex, a unit of Slim's America Movil, reiterated that new hires would get a pension on retirement worth 100% of their final net pay, determined by their job category, becoming eligible after 35 years of work and once they turn 65.

That sum would be made up of the pension paid out by the Telmex contract plus worker entitlements with state social security benefits, it said.

Workers who retired after 30 years would receive 75% of their final net pay, it said.

Union representatives of the Mexican Telephone Workers Union, known as STRM for its Spanish acronym, were set to vote on the proposal later on Tuesday, the union's spokesman said. If accepted, the proposal will go to all union members for a final vote.

The union, which represents 60,000 active and retired workers, began a two-day strike on July 21, the first in four decades, after talks with Telmex broke down over issues including salary raises, unfilled job openings and benefits for new hires.

The strike ended the next day following government mediation after the two sides agreed to continue negotiations.

(Reporting by Cassandra Garrison; editing by Richard Pullin)