The Scotland international's agent, Phil Graham, told the Daily Record, "It is correct to say Celtic are interested in Gareth. They have registered that interest officially with Nottingham Forest.
"At the moment the player is not for sale but we all know that things change in this game.
"I am sure if a realistic offer is made Forest would seriously consider it.
"It would be a hard decision for Gareth to make if he was given the choice of Celtic or perhaps Tottenham as both Spurs and Newcastle have registered their interest."
Forest rate Williams at £4 million.