There has been plenty of talk about the 35-year olds future in recent times and the new offer has been put on the table since it has been clear that Boro would stay in the top flight.
Speaking on the official club website, manager Southgate said, "Mark is at the end of his current contract and we decided we would make him an offer. It was difficult to do that when we didn't know what division we would be in.
"And I had to think long and hard about whether I wanted Mark to stay and whether that would impact on the other goalkeepers we have at the club. But if we can keep him it would be good, his experience is important to us."