Hi!
You're getting a lot of answers from the US above.
Not so useful in Cyprus.
Don't mention the car again and continue with the interview process. Don't offer to buy a car. Accept the position/sign the contract while ensuring that it states that you don't need to provide a car and have them cover the lease/insurance on a motorbike/scooter when push comes to shove.
I'm a little surprised that a decent sized firm won't provide a lease car. The cost of personal reimbursement per mi/km is much more prohibitive and a lease car is a simple business expense.
Is this a rinky dink firm?