Hooper scored six Premier League goals for Norwich last season, and Aston Villa, Crystal Palace and newly-promoted Queens Park Rangers have all been linked with the 26-year-old.
There have been reports that Hooper handed in a transfer request following Norwich's relegation to the Championship, but Adams has denied those claims.
Adams, who was confirmed as Chris Hughton's permanent successor at the end of the season, has told Hooper he could play an influential role in Norwich's bid for an immediate return to the top flight.
"There's been no transfer request from Gary Hooper," Adams told the Pink 'Un.
"I spoke to him two days ago and told him he's one of the players we need to keep. He can score goals, Gary Hooper can. He will be a big part of the squad, along with many, many others.
"So I understand - there's bound to be this sort of speculation and rumour, and somebody can make a throwaway comment that suddenly becomes national news.
"But Gary Hooper has not handed in a transfer request and I've told him I need him here to hopefully be part of pushing this team back into the Premier League, and he was happy with that."