First, you can, of course, be sued. Whether the lawsuit will survive a motion to dismiss, still less prevail at trial, is a totally different issue.
"It happened in the street, in front of my property, and it was the one time, I didn't have him on his leash"
Which is to say, your dog was unrestrained in a public way. Presumably the other dog was, also. This suggests a certain level of liability.
As you have offered to pay for the damages, there would be no apparent reason for the other dog's owner to sue. If they do, notify your homeowners insurance company.
The foregoing is for general information purposes and does not establish an attorney-client relationship.
Yes, you can be sued. You can also be cited for your dog being off leash and biting a domestic animal. If the other dog was on a leash, it makes the citation even more likely. In the civil suit, damages are apt to be limited to the veterinary bills or the value of the dog. If the person brings a claim against you, your homeowner's or renters insurance will likely cover it.
This is not to be construed as legal advice. I do not have an attorney client relationship with you.
Anyone can sue anybody for anything - the issue is whether the suit would be successful and the answer to that is always "it depends". While your dog is entitle to be unleashed while on your property you are still required to have full control of him, meaning he doesn't run into the street and attack another dog. If the other dog was also unleashed, then you both are liable; but if the other dog was on a leash then you are fully liable.
If the other owner accepts your offer of payment I suggest you do so with a signed agreement that the payment is in full satisfaction of any and all claims arising from the incident. You may want to speak with a local attorney regarding proper wording.
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.