Hendrick and Bardsley are out of contract at the end of this month and boss Sean Dyche would like to keep both at Turf Moor.
However chairman Mike Garlick and his board are being cautious because they do not yet know how much football's shutdown will cost them in lost revenue.
They are only prepared to offer the pair short-term contracts until the end of the current campaign later this summer.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!