Griffiths has fallen out of favour with Wolves manager Kenny Jackett in recent weeks but Celtic will have to offer more for the Scotland striker.
A post on Wolves' official Twitter account read: "Kenny has confirmed that Celtic have made a bid for Leigh Griffiths which has been rejected. Striker remains in squad for Oldham game."
Griffiths has scored 13 goals for Wolves this season but he has only started two of the last seven matches, since Jackett criticised his work-rate after taking him off at half-time in a defeat by MK Dons.
The Scotland international did not come off the bench during Wanderers' Sky Bet League One win over Bristol City on Saturday.
Griffiths last week stated it would be an "honour" to play for Celtic and admitted he wanted more certainty about his future at Wolves.
The former Livingston and Dundee striker scored 28 goals for Hibernian in his second loan spell with his boyhood heroes over the last two seasons.
The 23-year-old signed a new two-year contract at Molineux in August, with the option of another 12 months.
Jackett would not rule out selling Griffiths if a higher bid came in.
The Wolves boss, quoted on his club's Facebook page, said: "We've had a bid from Celtic which has been formalised but the club have turned it down.
"We do understand every player has their price but we are not desperate to sell players here.
"Leigh has gone public to say he is interested in the Celtic situation as most Scottish lads would be when a club of that size come in.
"But the deal would have to be right for us and we will have to see how it goes. If not Leigh is still part of our squad and is with us for Oldham tomorrow and Bradford on Saturday."
Celtic manager Neil Lennon revealed that talks between his club and Wolves were "ongoing".
When asked how far apart the clubs were, he said: "I have no idea. All I know is there was a bid went in.
"So we have made our intentions clear and the talks will keep going now for however length of time it takes to get a resolution one way or another.
"We will see if we can get a deal thrashed out."
When asked what Griffiths would bring to Celtic, Lennon said: "Goals. He had a fantastic season last year. I think he has improved as a player and there is scope for him to get better."