A lot of gamers have stated that the original Crysis could not run on consoles. However, one modder begs to differ. A user by the name of MrUpload has uploaded a video of the first level running on the PS3 using the Cryengine 3.
Unfortunately, this is still a work in progress as you will notice lighting issues and other incompatibilities since the author literally took the level and combined it with Crysis 2's engine. However, one glaring issue that seems to be irrelevant to the quality of the port job is the draw distance.