In Russian this sentence can have the both meanings. Depend on the context.
The choices that are more widely-used in Russian :
"I am looking for a wife" (means you don't have one) - "я ищу себе жену"
"I am looking for my wife" (means you already have one) - "я ищу свою жену".
But usually these choices can be interchangeable
As I know, the words "searching for" imply more endeavour, than the "looking for". Based on this "I am searching for my wife" in Russian would be "я разы́скиваю свою́ жену́". But these sentences usually can be interchangeable in Russian, it depends on the context. Press the report button next time.