The alleged crimes took place during McClain's recent six-month mission at the International Space Station.
Worden told the Times she learned McClain accessed her accounts because McClain had intimate knowledge of her spending. To confirm her suspicions, Worden had her bank locate computers that had accessed her account; one such access point came from a computer registered with NASA.
McClain, who returned to Earth on June 24, denies wrongdoing, although she admitted in an sworn interview last week that she did access the account from space.
"She strenuously denies that she did anything improper," McClain's lawyer, Rusty Hardin, told the Times.
Instead, McClain claims she was doing what she has always done: checking her family's finances to ensure there were sufficient funds in the account to pay bills and care for the son that McClain and Worden have raised together.
Hardin said McClain has routinely checked the account and was never informed she could no longer access it.
McClain and Hardin are in the midst of a heated custody battle over their 6-year-old son, who was conceived via in vitro fertilization and carried by a surrogate. Their divorce is set to be finalized in October, NBC News reported.
NASA did not comment on the ongoing dispute, although they praised McClain in a statement. McClain is a candidate for future lunar missions.
"She did a great job on her most recent NASA mission aboard the International Space Station. Like with all NASA employees, NASA does not comment on personal or personnel matters," NASA said.