According to ESPN.com's Buster Olney, La Russa has signed a multi-year contract to return. But Hal McRae will not return as the Cardinals hitting coach and will be replaced by McGwire.
"We're getting closer," La Russa told ESPN.com on Sunday. "But nothing has been decided yet. I can't tell you anything yet."
La Russa's two-year, $8.5 million contract expires at the end of the month.
McGwire, 46, has been out of baseball since 2001. In 16 seasons, he slugged 583 home runs, including what was then a single-season record 70 in 1998, and finished with a .263 career batting average. He has been repeatedly invited to serve as a Spring Training instructor for the Cardinals, but has declined. McGwire has worked with St. Louis' Skip Schumaker, among others, during the offseason.
The Cardinals were expected to announce this week whether La Russa would return for his 15th season managing the team, the St. Louis Post-Dispatch reported.
La Russa told the newspaper he is "speeding toward a decision" on whether to return but had not discussed a contract with Cardinals chairman Bill DeWitt Jr. However, the newspaper quotes "sources familiar with the situation" as saying a formal announcement that La Russa will return was expected early this week.
La Russa has been in contact with Cardinals general manager John Mozeliak. With Mozeliak expected to talk with Cuban left-handed pitcher Aroldis Chapman on Monday in New York, the paper reported it's unlikely an announcement regarding La Russa would be made before Tuesday.
In recent years, La Russa has operated under two-year contracts, which allowed him or the club to walk away from the deal.
La Russa ranks third on the all-time managerial wins list with 2,552 victories, behind Connie Mack (3,731) and John McGraw (2,763). His 4,772 games managed with the White Sox, Athletics and Cardinals rank second to Mack's 7,555.