He is looking for HIS suitcase (it's lost) or he is looking for A suitcase (he wants to buy one). The answer you provide is only correct in a specific context (someone else lost a suitcase and he's looking for it; someone else recommended a specific suitcase to buy and he is looking for it).
Both ‘a’ and ‘his’ should be accepted, I think.
I think "a", "the" and "his" are all acceptable since they are grammatically correct, even though some are more common and meaningful without a context than others.
I added "his" as a possible translation, thanks!
Note: there was another exercise with "a/the/her umbrella", so I doubt "his" here wasn't included on purpose :) Just inattentiveness.