"He's touch and go," Dyche told a news conference.
"They were messing around on a head tennis game and he caught the edge of the table and unfortunately cut his leg quite badly. We'll make a decision on him probably tomorrow.
"The modern table is a very fine bit of equipment but just misused on this occasion by accident but I'm not remotely questioning the equipment."
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Defender Matt Lowton, who stepped in against Bournemouth to make his 100th appearance for the club, could feature again if Bardsley is unavailable.
Striker Peter Crouch will miss the clash as he recovers from appendix surgery.
Dyche was hopeful winger Aaron Lennon could play again this season after a knee operation in December.
Burnley are 14th in the standings with 36 points from 33 games, four places and eight points above 18th-placed Cardiff.
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Pritha Sarkar)
