The intention should be for ‘Umrah Tamattu‘, not Hajj itself.

This is because in Hajj Tamattu‘, one performs ‘Umrah first, and then later, at the appointed time, re-enters ihram for Hajj from Makkah.

A heartfelt intention is sufficient, but saying “Labbayka Allahumma ‘Umrah” along with the talbiyah is recommended.