Tigers manager Peter Taylor says he is keen to keep the 25-year-old after netting his third goal in City colours on Saturday
Taylor said: "Michael didn't do himself any harm with that goal.
"I'll be sitting down with him to discuss his position and hopefully we can agree terms with him.
"There is no fee involved as Wolves are prepared to let Michael go and we'll just have to see how things pan out."
Branch himself is looking forward to being a Hull City player: "I'm really happy at Hull. Everything is agreed with Wolves and as far as I'm concerned it will be sorted out early this week.
"I want to come here. I know it's the Third Division but this club is definitely going places under Peter and I want to be part of it."