Those who purchase the Legacy edition of Call of Duty: Infinite Warfare, which comes with the game and the remastered version of Modern Warfare, will need 130GB of free space to install and play both games.
As you can see in the images below, the back of the PS4 version of the Call of Duty: Infinite Warfare Legacy Edition shows that a minimum of 130GB is required. Activision has yet to confirm the size of each game, but we do know that those who got early access to the campaign of Modern Warfare Remastered had to download 40GB. Assuming that these 40GB of Modern Warfare Remastered don't include the multiplayer portion, Infinite Warfare and the multiplayer portion should take approximately 90GB.
In comparision, last year's Call of Duty: Black Ops III required 55 GB, which is a lot less than Infinite Warfare plus Modern Warfare Remastered. However, it's also odd that the campaign of a remastered game alone takes 40GB of free space, which raises the possibility that the size could be related to the PS4 Pro and 4K support for Infinite Warfare.
Call of Duty: Infinity Warfare releases on the 4th of November on PS4, Xbox One and PC.