Ideally Barcelona need a 9 capable of playing long stretches of games from wide positions, be it right or left. They also need to be good with link up play. There is no imperative need for the player to be tall, nor does he necessarily need to be a prolific aerial scorer, these are just bonuses.
The main attribute really is the players capability to shift to the wide positions and retain his effectiveness.
South American forwards are the ideal mold because most of them can play many positions up front. Aguero and Suarez are the best examples, though they are very likely out of the list due to cost. Higuain is less capable of shifting to wide areas, but he is a very skilled and technically gifted 9, he could make it work, but again, would not be cheap.
Another similar mold to Higuain who could make it work would be Torres, moreso now with his newfound form. However Mourinho is in the middle, aka, not happening.
Then you have the other less versatile options of less flexible 9s, or pure scoring wingers.
I think the best approach for Barcelona is to use the new staff's knowledge of South American players and find a rising star who would fit the mold, and would both cost less and demand less once he arrives.