"Presso l'arancia ho una mela."
I would accept it.
We would never say "Presso l'arancia ho una mela", we would say "Vicino all'arancia ho una mela".
"Presso" is used for bigger things like buildings, shops, offices, apartments, et cetera.
http://www.wordreference.com/iten/presso If you check here, there is no "presso" with small objects in the examples.
Except "there is" is c'e', so we just have to assume the speaker is talking about an apple they have that is theirs, not just any old apple. Near the orange, I have an apple (that is mine).