Jones had 28 points during this season — the fourth most on the team — which included 23 assists, just three shy of Oliver Bjorkstrand's team leading 26.
"The Columbus Blue Jackets have asked him to consider if he would look at doing an extension at some point in this off-season," said Sportsnet's Chris Johnston during the Headlines segment of Hockey Night in Canada on Saturday.
"He's had some talks in the last few days with his agent Pat Brisson from CAA Sports, he's taking the weekend now to sort of mull it over and think things through, and I would expect somewhere here in the next few days he'll get back to the Blue Jackets about where he's at and whether he will entertain talks on an extension now."
Jones has been on the top defensive pair for Columbus with Michael Del Zotto playing alongside on the left.
Columbus finished the 2021 season in last place in the Central Division with an 18-26-12 record.