Is there any sparse language known to be in NPI under the $P \neq NP$ assumption ? I wonder to know wether there are sparse language (even constructed by delayed diagolanization) in NPI under the assumption that $P \neq NP$.
I don't know whether you are asking an open problem, or whether it has already been resolved. Yet the following paper can shed some light on this problem:

Kurtz, S. A. 1985. Sparse sets in NP-P: relativizations. SIAM J. Comput. 14, 1 (Feb. 1985), 113-119. DOI= http://dx.doi.org/10.1137/0214008

Basically, it states that, even assuming P≠NP, there is an oracle relative to which no sparse sets in NP-P exists. 

On the other hand, the following paper:

T. Baker, J. Gill, and R. Solovay, "Relativizations of the P=?NP Question", SIAM J. Computing (1975), 431-442. DOI= http://dx.doi.org/10.1137/0204037

demonstrates an oracle relative to which sparse sets in NP-P exists.

Since $NPI \subset NP-P$, this proves that, either way, the proof does not relativize.

EDIT: In addition, there exist sparse sets in NP-P if and only if $E \neq NE$:

Hartmanis, J., Sewelson, V., and Immerman, N. 1983. Sparse sets in NP-P: Exptime versus nexptime. In Proceedings of the Fifteenth Annual ACM Symposium on theory of Computing STOC '83. ACM, New York, NY, 382-391. DOI= http://doi.acm.org/10.1145/800061.808769

(Journal version available here: http://dx.doi.org/10.1016/S0019-9958(85)80004-8)