This can be enabled in v1.66 (it is in the Insiders now):

The editor.quickSuggestions setting now accepts inline as configuration value. When set to inline, quick suggestions (IntelliSense) don't display the suggestions widget when you type but show completions as ghosted text.

See v1.66 release notes: inline quick suggestions

In your settings:

  "editor.quickSuggestions": {
    "other": "inline", // the `inline` value is new
    "comments": true,
    "strings": true
  }

With this setting the suggestions will appear inline rather than as a pop-up.