Yes, you can, but using a random primer (NNNNN hexamer or octamer) included on each reaction, otherwise you will have only elongations in one direction of single strands, in final quantities depending of  the amount of template, but not really an exponential PCR amplification. Recommended to do first some 10-15 cycles only wiht the primer annealing on the known sequence and then add the random primer to achieve a dsDNA amplicon. The size of the PCR product wished upstream or downstream can be enriched by playing first with the elongation times of the PCRs. Important to leave some bases downstream of the annealing site of each primer as label of the targeted known gene. This helps to confirm the proper origin of your product. Otherwise is difficult to know after sequencing if you got a product from that gene or from an annealing site elsewhere.

Thanks Howard,

Another issue is that I am doing only first strand of the cDNA. Can this implicate? Do you think is possible to do this in both 5' and 3' ends?