AT&T said the offer to the 27,000 Communications Workers of America members includes pension and wage increases, and keeps 401(k) contribution as well as above-market health care.
A representative of the CWA declined comment on the offer from AT&T because negotiations were still going on.
The latest offer from AT&T was to workers in Texas, Missouri, Oklahoma, Kansas and Arkansas.
AT&T is currently in discussions with the union for labor contracts covering a total of 80,500 of its employees. AT&T has a total employee base of about 299,000 people.
Shares of AT&T were down 1.6 pct to $25.32 in noon trading on New York Stock Exchange.
(Reporting by Sinead Carew; Editing by Tim Dobbyn)