Both players are currently restricted free agents.
The 25-year-old Domi spent the last two seasons with the Canadiens. He set career highs in goals (28), assists (44), and points (72) in 2018-19, and managed 17 goals and 27 assists in 71 games last season.
Anderson, 26, appeared in just 26 contests in 2019-20 due to injury, recording one goal and three assists. He also set career highs in goals (27), assists (20), and points (47) in 2018-19.
While Anderson missed the majority of the 2019-20 season and the entirety of the playoffs, Blue Jackets general manager Jarmo Kekalainen recently said the forward is fully healed and would have played if Columbus advanced in the postseason, according to The Athletic's Aaron Portzline.
Domi, who expressed his desire to play center during his time in Montreal, figures to slot down the middle in Columbus.
"Strengthening our center ice position has been a priority for our club and we are extremely excited to add a player of Max Domi's talent and character to the Columbus Blue Jackets," Kekalainen said. "He is a skilled playmaker that also brings grit and competitiveness, and we think he will be a great addition to our team."