"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.