http://www.pcgamer.com/dark-souls-remastered-wont-have-cross-play/

Following the PC reveal of Dark Souls: Remastered, there was talk of discounts for owners of the original game. Bandai Namco told us this wasn't the case, a community manager said price cuts were unconfirmed, before a different spokesperson said "there is no official discount announced for the title at this time." Clearly this story has more open ends than a Souls side quest. 

What appears to be more certain, praise the sun, is the question of cross-play. With the Souls remaster set to feature on consoles and desktops alike, the folks at IGN raised the matter of online crossovers with the publisher.