SAN DIEGO -- Though the Chicago Cubs' front office indicated it would be attempting to complete extensions this offseason for several of its players with two years of club control remaining, that apparently doesn't apply to first baseman Anthony Rizzo.

Rizzo, 30, is beginning the first of two option years but would like to be a Cub for a lot longer.

"The Cubs have informed us that they will not be offering Anthony an extension at this time," Rizzo's agent, Marc Pollack, said from the winter meetings. "Anthony has let his desire to be a Cub for life known to the organization. Although we do not know what the future holds, a deal to make that happen will not be addressed now."

In an offseason in which teammates Kris Bryant and Willson Contreras have been mentioned in trade rumors and the team has turned over its manager and coaching staff, players such as Rizzo and shortstop Javy Baez would be logical candidates for contract extensions. The Cubs want to open a new window of contention after consecutive disappointing seasons, and Rizzo would like to help lead the way. Without an extension, free agency becomes a reality for him after the 2021 season.

On Tuesday, Cubs general manager Jed Hoyer indicated talks are happening with some players.

"Are we having those discussions? Yes," Hoyer said. "I'm not going to specify who or what, but certainly those conversations are ongoing."

Just not with Rizzo, according to his agent.

The former All-Star signed a seven-year, $41 million deal in 2013, just weeks into his first full season in the big leagues. His two option years will pay him an additional $33 million, but he's outperformed his contract, averaging 28 home runs, 96 RBIs and a .877 OPS. He's also a three-time All-Star, three-time Gold Glove winner, a Clemente Award winner and the de facto captain of the team. According to FanGraphs, he's been worth $221 million of value over the length of his deal, 18th best in baseball over that timeframe.

Rizzo's cumulative 28.2 WAR since 2013 is fourth to Paul Goldschmidt's 35.8 among first baseman, and the latter star signed a five-year, $130 million deal with the St. Louis Cardinals in his age 32 season. Rizzo will be the same age when his two team options are complete. It would seem that he would take a similar deal, or one close to it, but the longer the team waits, the more likely it is that the Cubs would lose him to free agency.

Another Cubs player who's up for free agency after 2021, left fielder Kyle Schwarber, also hasn't been approached regarding extension talks, according to an industry source. So that leaves Baez as the lone candidate for a new deal. Rizzo would like one as well.

"Anthony loves playing for the Cubs fans and loves the city of Chicago," Pollack said. "He is excited to be playing for David Ross and will continue to work hard to help the team get back into the postseason and win another championship."