Although it will not ship with the functionality, NeatherRealm have said that they hope to patch in cross-platform play to Mortal Kombat 11 at some point after release. The subject was briefly discussed with Game Designer Derek Kirtzic, but no details were given.
In other Mortal Kombat 11 news it has been confirmed that the beta will only be available on PS4 and Xbox One. The recently published FAQ for the game states the following:
The Mortal Kombat 11 beta will allow players who pre-order to access an early sample of Mortal Kombat 11 before the game launches. The beta for Mortal Kombat 11 will only be available for PlayStation 4, PlayStation 4 Pro, Xbox One and Xbox One X.