The Canaries are looking to bolster their attacking options during the January transfer window, and have lodged bids for Swansea forward Danny Graham as well as Celtic striker Gary Hooper, with an improved offer on what is understood to have been an initial £5million deal knocked back by the Scottish club.
Leeds frontman Luciano Becchio, who has handed in a transfer request, and QPR forward Jamie Mackie are others said to be on Hughton's radar.
Sierra Leone international Kamara had a trial with Stoke in December, but was not offered a deal, and Norwich could now be ready to offer the 28-year-old a chance to play in the English top flight should a deal be struck with the Major League Soccer side.
"Kei Kamara is a player we have made enquiries about, but any progress remains behind closed doors," Hughton said at a press conference ahead of Saturday's FA Cup fourth-round tie against Luton.
Norwich announced on Wednesday that goalkeeper Lee Camp was set to sign following his release from Nottingham Forest.
The 28-year-old Northern Ireland international will provide experienced cover as John Ruddy continues his recovery from a thigh injury.
Hughton is determined to keep a lid on any transfer developments over the closing days of the January window, but accepts the club are sometimes swimming against the tide of continued speculation.
"Generally 99 per cent of what is in the media has no fact. Any progress or not will take place behind-the-scenes," the Canaries manager said.
"If and when there is any definite news, we will get it to you."
Celtic manager Neil Lennon revealed the Scottish club had rejected a second offer from Norwich for Hooper, whose double strike against Dundee United on Tuesday took his tally to 22 for the season.
Hughton, though, would not discuss the matter further when pressed by reporters.
"This is something that got into the public domain and sometimes it is difficult to stop. We are where we are on that one," he said.
"People now know what the facts are. Yes, there was a bid put in. The rest we will have to wait and see.
"What I can control is what I tell you now. Anything we try to do is done very much club-to-club and we try to do as much as possible in the appropriate way."
Norwich have not won in the Barclays Premier League since beating Wigan on December 15 and - following the 5-0 mauling at Liverpool - have lost five of the last six as they start to look anxiously over their shoulders on the battle at the wrong end of the table.
This weekend, though, offers a short respite with the chance to progress into the last 16 of the FA Cup as they host Blue Square Premier outfit Luton.
As in the last round at Peterborough, Hughton confirmed he would make full use of his resources.
"It will be a strong squad. I just need to determine which 11 will start," he said.
"Whatever changes I make if I look at the 18 players they will be all ones who have been involved in the first team."
Full-back Steven Whittaker has resumed full training this week after a hip problem and so could come into contention for a first appearance since December 22.
Centre-half Sebastien Bassong has been troubled a calf injury and so may be rested ahead of next Wednesday's visit of his former club Tottenham.
Striker Steve Morison (thigh) remains sidelined.