The 22-year-old striker will see his current deal at Molineux expire at the end of the season, but Wolves have a one-year option on him.
Dean Saunders intends to activate that clause after seeing Griffiths star for Hibs.
He took his goal tally for the season to 25 on Saturday as he bagged a brace in a thrilling Scottish Cup semi-final victory over Falkirk, and Wolves are hoping he can deliver more of the same for them next season.
Saunders said: "We will be taking up the option on Leigh. He scored a great goal in the semi-final and has done well for Hibs.
"Obviously he is playing a different level but it is progress for him. Goalscorers are hard to find and he has a fantastic record up there this season.
"I am really looking forward to working with him when he comes back for pre-season.
"I have told him if we could have got him back when Sylvan Ebanks-Blake broke his leg at the start of April we would have. But when we extended his loan we had to do it window to window.
"When he came back after I had just taken over, I had to make a decision on what to do in a few days. At the time he was about fifth choice striker and I was looking to bring someone else in. So it was better for his career to have that loan extended.
"Hindsight is a great thing and if we had known then what we do now, we would have kept him."