Gibbs-White played a starring role as the Blades reached the play-offs in the Championship, scoring 10 goals and producing 12 assists in 37 appearances.
Now, Wolves are keen to reward the 22-year-old for his progress and make him an important part of Bruno Lage's squad.
Gibbs-White, who came through the academy ranks and has played 86 times for Wolves, signed a contract extension last summer before heading to Bramall Lane.
Fresh terms have now been offered to the attack-minded midfielder, who Lage tried to tempt back to Molineux in January before he ultimately saw out the season with the Blades.
Lage has recently held discussions with Gibbs-White and said on him last week: "I was very happy with Morgan. I will not treat him as a kid because now he’s a professional and he’s a man.
“When Hwang (Hee-chan) came he understood that maybe he didn’t have the space to play so he went on-loan and did a fantastic job.
“In January I did everything to convince him to stay here. It was very clear and I gave him space and time to think about it.
“At the end of January we spoke and between him, Scott (Sellars) and me, we decided he would go and finish the season there. After we will see. If I want him in January, I continue to want him here because he can be an important player for the club."
Lage added: “He’s one of the players that comes from the academy and I know it’s so important for the club to have that. I am a foreigner and we have a lot of foreign players but it’s important for the club to have players from the academy and born in the UK, because they love Wolves more than me because they grew up here.
“I am here just one year and love to be here but the way players like Morgan loves the club is in a different way.”
Gibbs-White, from Stafford, won the Blades' player of the year award and previously had a loan spell at Swansea City.