Will my current lender re-fi my ARM, which is about to go up

My 5 year arm loan is about to change in October. This will result in our monthly payment increasing by $300 per month. Payoff amount is $216,000.00 yet the propertytax value is only $182,000.00. The gentleman I spoke with (from our current lender) seemed positive that he could help but I do not know anything at this point. I have given him all of our information and he was waiting to see what our credit scores were. Said he would call me back.

Based of the information given, does this sound realistic?

Thanks in advance for any advice.