MediaTakeOut has posted pictures of the 25-year-old rapper and 38-year-old former model at a restaurant in Disneyland.
Since the release of his first album Thank Me Later, Drake has been linked to female celebrities including British singer Rita Ora and rapper Nicki Minaj.
Banks, who recently fired long-time America's Next Top Model judges Jay Manuel, Nigel Barker and Miss J, ended her relationship with businessman John Utendahl earlier this year.
Both Drake and Banks have yet to confirm or deny the rumours.
For his sophomore album Take Care, Drake collaborated with Rihanna, whom he has also been linked to in the past.
Watch Drake and Rihanna in the video for 'Take Care' below: