And Nationals pitcher Stephen Strasburg, the World Series MVP, could be joining them in the next few days. He has the right to opt out of his contract, which has $100 million over four years remaining.
Baseball's business season starts shortly after the final out.
"I think it's hard to kind of fast-forward," Astros manager AJ Hinch said. "Seasons end really fast. I don't care if you get all the way to the seventh game of the World Series. It's all of a sudden -- boom! -- it's over."
Cole, Rendon and Strasburg all are represented by Scott Boras, known for slow, methodical negotiations. Last winter, he reached outfielder Bryce Harper's $330 million, 13-year deal with Philadelphia on Feb. 28.
Cole, a 29-year-old right-hander who went 20-5 this year, is expected to get a record contract for a pitcher, topping David Price's $217 million, seven-year deal with Boston before the 2016 season and Justin Verlander's $31.33 million average salary under a three-year deal with the Astros that started in 2019.
Cole tweeted a letter Thursday praising Houston fans.
"Before I became an Astro, I didn't know much about Houston, but after just two years you have made it feel like home," he wrote. "This is a relationship between a team and ... fans like no other that I know."
Strasburg, a 31-year-old right-hander, just finished the third season of a $175 million deal, and at 18-6 he also is coming off his best season. Rendon led the major leagues with 126 RBIs while hitting .319 with 34 homers.
A total of 131 players became free agents Thursday, seven more were announced Friday, and another 46 could be eligible pending decisions on team, player and mutual options during the next few days.
Among the pitchers available are major league ERA leader Hyun-Jin Ryu, Zack Wheeler, Madison Bumgarner, Rick Porcello, Cole Hamels, Jake Odorizzi and Dallas Keuchel, who went free after the 2018 season and waited until June to reach a one-year deal with Atlanta.
Teams must decide by Monday whether to make $17.8 million qualifying offers to their former players who became free agents. Players are eligible for the offer if they were on the roster for the season and never received a qualifying offer before. The price dropped for the first time, by $100,000, following a second straight slow offseason for roster moves.
Edwin Encarnacion's $25 million option was declined by the Yankees, triggering a $5 million buyout.
Cleveland exercised Corey Kluber's $17.5 million team option and declined options on second baseman Jason Kipnis ($16.5 million) and reliever Dan Otero ($1.5 million). Kipnis gets a $2.5 million buyout and Otero a $100,000 buyout. Left-hander Oliver Perez's option became guaranteed at $3 million because he pitched in 60 or more games and passed a club physical.
Versatile Oakland reliever Yusmeiro Petit had his $5.5 million contract option for the 2020 season exercised by the Athletics, who declined their half of a $5.75 million mutual option on left-handed pitcher Jake Diekman, who gets a $500,000 buyout.