Relay control using Arduino Uno

Dear
I am new to Arduino, struggling to make a simple project and looking for your guidance.
My aim is to control a relay by sensing a motor status indirectly. That means if a motor runs my relay should on and continue for 10 min, if still motor on , without switching it should n for another 10 min.
To sense the my motor( noiseless) condition is there any way or is it advisable to put a small coil to power lines of motor status.
Please kindly advise

What device is controlling the motor? Reading that device?
Else current measuring circuitry is a possibility.
The 10 minute is preferably handle using the millis() function.

You have a good idea; to sense when the motor is using more electricity. This link shows how to use a current sensor with Arduino:
https://dronebotworkshop.com/dc-volt-current/

is it an AC or DC motor ? what voltage/power/current rating?