The Dutch striker was forced off four minutes before half-time in Chelsea's goalless draw at Tottenham on Sunday and initial suggestions were that he could be ruled out for between a fortnight and a month.
Manager Claudio Ranieri said he expected Hasselbaink to be out for a minimum of two weeks after the Barclaycard Premiership match at White Hart Lane.
But the club's television station insists assessment of the problem at the training ground on Monday showed the damage was 'not as bad as first feared'.
And Chelsea's top scorer for the past two seasons is rated 50-50 for the weekend visit of Birmingham to Stamford Bridge.