Hibs chairman Rod Petrie travelled to Wolverhampton last week to meet Wanderers chief executive Jez Moxey in an attempt to secure the services of the Scotland international, who scored 28 goals while on loan at Easter Road last term.
But Wolves firmly rejected the confidential offer and have no intention to sell Griffiths as they look to secure an immediate return to the npower Championship next term.
Petrie told Wolves' official website: "I wanted to come to Wolverhampton to meet Jez face-to-face to impress upon him the desire of Hibernian to acquire the services of Leigh Griffiths on a permanent basis.
"We had a cordial meeting and I put firm proposals on the table. However, these have been rejected outright. Reluctantly, we have to conclude that there is nothing further that can be done at this time to prise the player away from Wolves."
New Wolves head coach Kenny Jackett has already signalled his desire to work with Griffiths next season, with the Black Country club having in April triggered a 12-month option on his contract to keep the marksman at Molineux.
The 22-year-old earned the Scottish Football Writers' Association and Clydesdale Bank Premier League Player of the Year awards, among others, for his exploits at Hibs last term, his second successive season-long loan spell with his boyhood club.
And following Griffiths' success north of the border Wolves have no intention of relinquishing his services.
Moxey said: "Our new head coach Kenny Jackett is looking forward to working with Leigh, who has been such a sensation in Scottish football during his time with Hibernian.
"There is no offer which can be made at this time that will change our minds. Leigh will be returning to Molineux and will play his part in our pre-season friendly matches.
"More importantly, we want Leigh to score goals for Wolves in League One, just as he has done for Hibernian in the Scottish Premier League, and hope he will help the team to success this coming season."