Speaking to reporters on Thursday, Rizzo didn't provide his reaction to not receiving a new contract, but he did say the business of baseball is as "cutthroat" as ever.
Rizzo cited the trade rumors around Kris Bryant as evidence of MLB's cutthroat nature: "We're talking about trading the MVP of the league a couple years ago."
As things currently play out with the Cubs, Rizzo also said "it would be naive" to think he will finish his career with the organization.
Rizzo's agent, Marc Pollack, told reporters during the winter meetings in December that the Cubs informed them they weren't going to offer the three-time All-Star a new deal this offseason.
"Anthony has let his desire to be a Cub for life known to the organization," Pollack said. "Although we do not know what the future holds, a deal to make that happen will not be addressed now."
The Cubs exercised Rizzo's $16.5 million option for 2020 in November. He has another team option for the same money next year that the front office will decide on after this season.
Rizzo has been among the most valuable Cubs players since being acquired in a trade with the San Diego Padres in Jan. 2012. The 30-year-old hit .293/.405/.520 with 27 homers in 146 games last season.
Chicago did post its fifth straight winning season last year (84-78) but missed the postseason for the first time since 2014 with a third-place finish in the National League Central.