Konchesky was replaced at half-time during the Foxes' 1-1 home draw against Leeds on Tuesday night after complaining of tightness in his hamstring.
The experienced left-back underwent a scan on Wednesday and manager Nigel Pearson is awaiting the results.
Should Konchesky miss out, Pearson is expected to opt for Lloyd Dyer at left-back after the winger replaced him against Leeds. However, Jeff Schlupp could come back into the squad
Striker Schlupp, who is currently the subject of negotiations between Leicester and Manchester United about a possible move to Old Trafford in the summer after impressing during a month-long trial at the Barclays Premier League leaders, has been used as a makeshift left-back on several occasions this season.
Midfielder Matty James will also require a late check having missed the last four games with a knee problem.