The 19-year-old, who is on loan at the Walkers Stadium from Manchester United, has returned to the Premier League champions to be assessed after suffering a dislocated shoulder in the Foxes' 1-1 home draw against Colchester on Saturday.
Assistant manager Craig Shakespeare believes it is too soon to determine whether Cleverley will be available for the top-of-the-table clash at Peterborough at the weekend.
He told the League One leaders' official website: "Tom has gone back to Manchester United for further assessment. They will then make a decision later in the week.
"Admittedly it is not looking good, but let's not write him off yet because he is a strong boy. Tom is a strong lad who has got very good upper body strength."