The two dined together on Saturday (December 8) at Los Angeles eatery Cecconi's, according to The Insider.
Gavankar was apparently later photographed smiling as she entered Cowell's car after they finished their meal.
Cowell has most recently been romantically linked to Carmen Electra, who downplayed those rumours in November.
The X Factor USA judge ended his relationship with former fiancée Mezhgan Hussainy in February.
Gavankar - who plays Shiva on The League and Luna on True Blood - is an Illinois native, who is a singer in addition to her acting career.