Is it possible to opt for a balance transfer card from the same company with whom I owe an amount?

Usually, the purpose of a balance transfer is to acquire a new customer along with existing debt.
Alternatively, you can transfer your balance to your one of the lowest interest rate cards with sufficient credit limit.

This is never written in a credit card agreement letter, but understand this fact clearly. A bank won't allow you to do a balance transfer between 2 cards that it issued. The logic is simple. The objective behind a balance transfer is to get a new customer with an existing debt. They don't want that existing customers to avoid interest charges.

You can ask the credit card company about this. I think they will agree.