I was discussing this yesterday with friends: the building is still a church but a few years ago it was sold to the State (so the Church doesn't have to be responsible for the upkeep...). This means the State could, in theory, throw out all the Catholic paraphernalia and ripristinate a classical-looking interior, if local government so wished. We don't have images of the original Roman statues but I'm sure there are plenty that could be moved in from other locations. It would be definitely something that would stir international attention and attract more funds (always good) and more tourists (not always good - it's debatable whether one of the most-visited hotspots in the city actually needs more attendance...)
In any case, it will likely never happen; not only because of the massive outcry from religious quarters in "the" Catholic city, but also because a lot of the academic world is strongly opposed to this sort of "restauration" both on philosophical and practical grounds, after some massive missteps that lost us priceless artefacts in the previous centuries.
It's a shame, I think a classical Pantheon would be superb, but that's life.