However, both offers are for less guaranteed money than the two longtime Cardinals would've made last season, sources told Goold.
Team chairman Bill DeWitt Jr. acknowledged that at least one or both players may end up in a different jersey in 2021 for the first time in their major-league careers.
"(It's) their decision. Someone may come in and offer them more, and they may choose to take it. We will just have to see," DeWitt said.
Molina already said he'll "retire happy" if he doesn't get a contract that impresses him. The 38-year-old is a nine-time All-Star, nine-time Gold Glove winner, and owns two World Series rings during his 17-year run with the Cardinals.
The 39-year-old Wainwright, a three-time All-Star, has pitched with St. Louis for 15 seasons.