The forward has been a regular for Wolves since making a season-long loan switch from RB Leipzig.
Wolves have a £14million option to sign him permanently in the summer, but it is understood they have been keen for some time to make the deal in January.
Hwang is now sidelined until February with a hamstring injury and when asked if that will impact the plans to sign him, Lage said: “In my opinion, no.
“He is an important player for us and I am very happy with him.
“It is hard when you are playing and then you can’t work with your team-mates, but they know these kind of things happen.
“Hwang is a big professional who has a good mentality, and he will be strong.”
Wolves have a small squad and Lage has consistently reiterated his desire to make additions.
With the transfer window now opening, the head coach has outlined his plans.
He added: “We need one centre-back. Also we can find one more winger and a different striker.
“We have two or three situations we can improve to better manage our squad.
“This is my desire and what I want, to see how the team can grow up with players.”
Wolves only have three senior midfield options and when pressed on whether he would like to sign another, Lage insisted his focus was on the Manchester United fixture.
He went on to say that he would happily answer every transfer window question after that game on Monday.
Lage said: “We need some players and some positions. I want more competition in the team.
“The main thing is the players that are injured are fit for Wolves.”