According to the Lancashire Telegraph, Ings is expected to miss the rest of the month at least and Burnley want to bring in cover before the emergency loan window closes next Thursday, March 28.
"We have to look for a replacement if it's more serious or worse than expected," said Burnley co-chairman John Banaszkiewicz.
"We are in the market for loans for cover, with not many games left to play.
"The manager and recruitment staff are really focusing on that before next week's deadline."
Ings and Vokes have 38 league goals between them this season, helping Burnley to second in the Championship and 10 points clear of the chasing pack in the hunt for automatic promotion.