Your HP printer is showing “no internet connection” because it is not connected properly to your Wi-Fi network or it cannot access HP’s online services like HP Instant Ink, even if it might still print locally. This message typically appears when the printer’s wireless connection is off, unstable, or the printer cannot reach the internet despite being connected to the router[1][3].

Common solutions include:

1. Checking the printer’s wireless button/status light to ensure Wi-Fi is on and connected (solid blue light means connected)[1].

2. Restarting your printer and router to refresh the connection[1].

3. Ensuring your printer is connected to the correct Wi-Fi network and that the network internet is working.

4. Updating the printer firmware, as outdated firmware can cause connectivity issues with HP services[2].

5. Resetting the printer network settings and reconfiguring the connection if problems persist (note this will disconnect it temporarily)[2].

Additionally, if your printer reports no internet connection but can still print and scan, the issue might be with the printer’s access to external HP services rather than the local network[2][3].

For detailed step-by-step guides, HP provides official support videos and help pages which cover these troubleshooting steps thoroughly[1][3].