Hooper arrived at Carrow Road from Celtic at the start of the 2013-14 campaign, but failed to replicate his prolific form shown in Scotland, scoring just six goals in 32 Premier League appearances as Norwich were relegated.
Adams has bolstered his squad ahead of the Championship season with the signing of Lewis Grabban from Bournemouth, but the Norwich manager insists Grabban's arrival does not mean Hooper is set for the exit door.
"A transfer request from Gary Hooper hasn't happened," he told BBC Radio Norfolk.
"I've spoken to Gary - he's a goalscorer and we need goalscorers.
"He's part of a strike line-up that will be competing for places.
"I spoke to all the players at the end of last season. Virtually to a man they were all committed to the cause.
"They and I are realistic enough to recognise that after relegation there are offers for players. As yet there have been no offers put to me.
"If offers are ones you can't turn down or players want to leave we have to accept that, but I'm more focused on bringing players in."
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