No, Nina Dobrev is no relation to the Bulgarian footballer Dobri Dobrev, as far as I have been able to discover.
Dobrev is a common surname in Nina's home country of Bulgaria, and several well-known Bulgarians have shared Nina's surname. Bear in mind also that Nina's surname was originally 'Dobreva' before her family moved to Canada.
Dobri Dobrev appears to have lived in Bulgaria his whole life. He currently plays for FC Vitosha Bistritsa, who are based near the Bulgarian capital of Sofia.
Here's an interview with Nina in her home country of Bulgaria: