The Airbus A380 comes with two engine choices:
The thrust reversers are not part of the core engines. The reversers are developed by the company which produces the engine nacelle, in this case Safran Nacelles. They developed nacelles for both engine variants for the A380, including the first electrically actuated reversers:
Safran Nacelles nacelle systems equip the Airbus A380 powered by four Rolls-Royce Trent 900 engines or four Engine Alliance GP7200 engines. [...] they are the first in the world to have a thrust reverser with an Electric Thrust Reverser Actuation System (ETRAS®).
(image source: safran-group.com)
Are the nacelles interchangeable?
No, the nacelles for the outer engines are different from the inner ones to save weight. This article says:
Four nacelles were developed for the A380: one inboard nacelle (with a thrust reverser) and one outboard nacelle (without), for each of the type's two engines, the Rolls-Royce Trent 900 and Engine Alliance GP7200.
As ymb1 pointed out in the comments, this is confirmed by the type certificate for the Trent 900:
At engine certification, the engine has been approved for use with Aircelle Thrust Reverser Unit
(TRU) at the inboard engine positions (part numbers ASE 0010-XX-0 for the left hand installation
and ASE 0050-XX-0 for the right hand installation) and for a Fixed Fan Duct (FFD) in the outboard
engine positions (part numbers ASE 5010-XX-0 for the left hand installation and ASE 5050-XX-0
for the right hand installation).
The TRU and FFD do not form part of the engine type design and must be certified as part of the
aircraft type design.
and also for the GP7000:
This engine is approved for use with Airbus thrust reverser system P/Ns (left and right)
L78DR130000xxx / L78DR230000xxx and with Airbus fixed fan duct P/Ns (left and right)
L78DR140000xxx / L78DR240000xxx.