A method, apparatus and computer program product are provided that continue to obtain the power saving advantages provided by discontinuous reception, while obtaining the measurement samples that are desired during a sampling time period, such as during a time to trigger period, to determine of handover is appropriate. In the context of a method, a measurement sample is caused to be obtained during a discontinuous reception monitoring period. The method may determine that a sampling time period has been commenced based upon a measurement sample. During the sampling time period, one or more additional measurement samples are to be obtained. The method may also determine that the additional measurement samples will not be obtained prior to commencement of the sleep period between monitoring periods and, as a result, cause one or more additional measurement samples to be obtained at respective times that would otherwise have been in the sleep period.