Burnley's owners have offered to buy the shares in the club which are held by the Turf Moor side's fans.
Supporters own around 6% of the club and American investment group ALK Capital, who completed a takeover in December 2020, say there is no obligation for them to sell.
If all shareholders do accept, it would take ALK's stake in the club to 90%.
"We wanted to do the right thing by our fans and shareholders," said Burnley chairman Alan Pace.
"It would be a shame to not provide a considered offer to the group.