Today i found a purple sponge which closely resembles a cliona. However, upon looking through my ID guide of invertebrates within the Mediterranean. I was unable to find it.
Found next to a marina, deep purple, only osicles showing.
A picture would have helped a lot as a purple colored sponge with prominent osculi can be many; in fact, upon viewing your question I found Ailochroia crassa, Ianthella basta etc which are all purple in color but not common in the Mediterranean. There is also a species in the region named Petrosia ficiformis which is somewhat purplish and fits your description . Cliona viridis is native to the Mediterranean and appears darker reddish green due to the zooxanthellae and it may be what you saw. Another Mediterranean species is Dasydiea avara with beautiful purple coloration and a good contender to be your species.
I hope one of the species is what you are looking for.