If you had signed in to your Chrome with same account which you are using on your mobile then you will be able to get notification on desktop too. If you don’t want to get notification and looking a way to disable it then you could do it by simple tweak.
Temporary Disable :-
If you want disable it temporary then just right click on a bell icon placed on your taskbar and select any one of the listed options:-
- Do no disturb
- Do not disturb for one hour
- Do not disturb for one day
Permanently Disable :-
If you wants to disable permanently then :-
- Launch Google Chrome and type chrome://flags and hit enter
- Now search for Enable Rich Notifications and from drop down menu disable it and restart your browser,
- That’s it, you had disabled Google Now notification on Google Chrome desktop
Google must have gave an option to user so that users can decide whether they want notification or not.