It sounds like you've been living beyond your means!
To answer your question, yes, you should be very careful.
Are they asking for a "secured" loan? Or asking for a guarantor?
In that case, they're trying to turn unsecured debt into secured debt. i.e. if you rang them tomorrow and told them you have no money, they have limited options about chasing you for the overdraft.
If however they managed to get you to sign a secured loan (secured against your house, for example), or get a guarantor, they'd be able to chase that money down.
Otherwise, the only other reason I can think of is to move you to a higher interest rate.
BTW, the Credit Card and over-draft debts are with two different parts of the bank.
The people offering you a loan to clear your overdraft probably don't care about your credit card debt.
Typically a credit card would be about 16-19% interest, whereas an overdraft might be 9-14%. Can you confirm?
So it would be more beneficial to you to clear your credit card debt. Again, a credit card is also unsecured lending, so be careful. But only if you don't use the credit card again.
You could end up in a world of trouble if you take loans to clear the overdraft or the credit card, but without amending your spending, you would end up in even more debt, as you would be spending the same amount on living expenses PLUS repaying the loan. You might end up back where you are right now, with a new debt on top of all the other ones.