In this paper, based on theoretical estimation of the achievable electric fields during the physical development process of a long spark under different conditions, we show that the encounter of negative and positive streamer fronts just before the final breakdown is one scenario, under which the observed X-ray bursts in long sparks is highly possible. Our calculations show that for example in an 80 cm long rod-sphere air gap at atmospheric pressure with negative lightning impulse breakdown voltage of about 925 kV, electrons are accelerated to values in the range of 100-300 keV during the encounter. Subsequently, these electrons gain more energy moving through the potential gradient of the positive streamer region. The total gain of energy by electrons may reach 300-500 keV. The results also show that negative discharges can produce more energetic electrons than positive. If the suggested mechanism of X-ray production in long sparks is correct, then the X-ray burst may consist of several pulses closely spaced in time. Time resolved photography in simultaneous measurement of X-rays would be able to confirm this prediction.