The 27-year-old Brazilian was back in Holland this week as AZ Alkmaar continued their battle for compensation after losing out on his signature.
However, with the long-running saga set to continue at an arbitration hearing on May 19, Southgate is confident his striker's mind is fully focused on his club's mission to claim the points they need to end their relegation fears at home to Portsmouth on Saturday.
Southgate said: "I only know what I have read. I was aware he was going for part of this court case this week.
"He is very relaxed about it. It doesn't entail our club, really, but we are there to support Afonso if he needs it.
"But he is very calm about it. He doesn't feel there is anything to answer.
"The Dutch FA gave their verdict on it before he came to us, so it's an unfortunate side-show, but not something that he seems too perturbed by."
Asked if he feared the court proceedings would affect Alves on Saturday, Southgate replied: "Not from what I have seen, no."