How to Make Your Web Browser Stop Asking You to Save Passwords. Hopefully, you are using LastPass or similar software to remember your passwords, and to keep them secure. The computer is far better at remembering passwords than you are; and, you should be using LastPass to do it for you. Once installed, however, you don't need to have Chrome prompting you to save passwords all the time. LastPass will do that for you. This tip will show you how to turn the reminder off in Chrome. Be careful out there.