Thanks for the report.
This is passwords issue, so changing the component.
Also -- triaging for passwords team works without assigning owners to issues unless somebody starts working on it. Being in our component and available means being in the TODO list. I'm adjusting that as well.

Just to be clear, the issue appears to be both Chrome iOS is not asking to save passwords AND is not offering to FILL passwords that are saved.  In other words, if you have passwords saved in your Windows Chrome / Google account and they are syncing to the iOS device iOS chrome is never offering to autofill

1. On iOS Only save passwords is not asking to save passwords AND is not offering to FILL passwords that are saved.
2. Even when the account is synced from desktop to iOS device, Chrome is never offering to autofill.

nothing really different to add .. just that my chrome browser on my iPad mini (v10.3.1) does have the id and password fields already populated (only if they were previously saved on my desk top chrome browser) .. but still, neither device will ask to save, nor remember, id and password fields

Just wanted to add that the issue is still present in Chrome v60.0.3112.89 on iOS v10.3.3 . Passwords will not save when entered on the iOS client, nor will passwords auto fill with synced data. The Chrome iOS client will retrieve saved passwords from other clients (Android, Windows) under settings, but it will not use the data to fill forms on the corresponding sites.

Can confirm on Chrome v62.0.3203.60 with iOS v11.1.1 that this issue still persists. Only tested password saving for local device only (iPhone 7). Did not try syncing passwords from a google account.