The Dutch international is reported to have had a falling-out with Southgate after he was omitted from the Boro squad to face Everton on New Year's Day.
"George is back in the fold today and that's the way we want it. As far as I am concerned he is a Boro player. He's also an experienced player and part of our squad," Southgate told the Evening Gazette.
"He's been disappointed and I understand that, but we all have a job to do and we have to work together and move on.
"George was disappointed with that and he was not in the right frame of mind to be involved at Bristol City.
"He is a bit emotional and we will have to see what the long-term future holds.
"We have a big game against Liverpool on Saturday and I want everybody possible available so that we can do everything we can to try to win the game."