Watch for IP Used to Contact Sublime
$ sudo netstat -nputwc | grep subl
Example Output:
tcp 0 0 10.211.55.6:46296 45.55.255.55:80 ESTABLISHED 337/sublime_text
tcp 0 0 10.211.55.6:46296 45.55.255.55:80 ESTABLISHED 337/sublime_text
Block with iptables
$ sudo iptables -A OUTPUT -j DROP -d 45.55.255.55
List your iptables
$ sudo iptables -S
Older Methods No Longer Work
Refer: https://stackoverflow.com/questions/35269327/how-to-disable-new-version-notifications/35269421
go to Preferences -> Settings-User and add there: "update_check": false
EDIT :
If it's not working then add this line 127.0.0.1 www.sublimetext.com in your host file
File Location
Windows : c:/windows/system32/drivers/etc/hosts
Linux : /etc/hosts