Bochy ranks 11th all-time in managerial wins with 2,003 across 25 years between the Padres and Giants.
The 64-year-old former catcher recorded a 951-975 record in 12 years with San Diego and a 1,052-1,054 mark in 13 seasons with San Francisco. He won three World Series titles with the Giants in a five-year span (2010-2014) and was named 1996 NL Manager of the Year with the Padres.
"In my mind, it's time," he told reporters when he announced he'd retire after the 2020 season last February "I've managed with my gut and came up here in 2007 on my gut. It's a gut feeling that it's time. It's been an unbelievable ride, and there's so much that I can be grateful for."
In September, Bochy remained steadfast in his plan to leave the Giants at season's end, but didn't completely close the door on a future comeback.
"I've said I'm good, but later on as you get away from the game, who knows how you react," he said. "I don't think anybody knows until you get to that point."
The Astros and Red Sox are both looking for new managers after their respective sign-stealing scandals.
Houston fired general manager Jeff Luhnow and manager AJ Hinch after they each received a one-year suspension for the club's 2017 scheme, which included the use of technology to steal opposing signs and relay them to hitters via loud noises from the clubhouse tunnel.
Boston and manager Alex Cora, who served as the Astros' bench coach in 2017 before joining the Red Sox in 2018, "mutually agreed" to part ways amid an MLB investigation. Ken Rosenthal and Evan Drellich of The Athletic reported it's related to the alleged unsanctioned use of their video room in 2018.
Both clubs won the World Series in the season probed by the league.
Bochy would represent a stabilizing force for either team amid the turmoil, but it doesn't sound like he's ready for a comeback.