The club are crossing their fingers that the former England international is not going to see a premature end to his season.
Dunn picked up a calf problem during Monday night's 1-0 home defeat by Manchester City and was replaced by Ruben Rochina in the second half.
Dunn is in the treatment room being assessed by the medical staff, but the bad news is he is currently rated as a ‘major doubt’ ahead of Saturday’s home game against Bolton Wanderers.
"David felt a strange feeling in his leg and came off," said Kean to Sky Sports.
"We are hoping it is only fibres, rather than anything more serious."