Winger Redmond, who joined Norwich from Birmingham City in the close-season, and winger Pilkington are both said to have attracted the interest of the Welsh club.
However, Hughton was quick to dismiss that speculation, insisting that he has no desire to let either player leave Carrow Road.
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"Nathan is very happy here," Hughton said ahead of Tuesday's clash with his former club Newcastle United. "He is one who has had a lot of involvement here.
"He is a very well-grounded young man who is improving his game week in, week out. He is a very mature young man and we are delighted to have him here and he wants to develop and improve here.
"Any potential rumours for our players is a testament to what we are trying to do here. It is not welcome, of course, but we must be doing something right, but there is no fact in any bid for Anthony from Swansea."
Norwich are thought to be keen to reinforce their defence, with Blackburn Rovers' Scott Dann and Newcastle's Steven Taylor touted as potential targets.
Hughton swiftly denied talk of a bid for Dann, but was coy on prospective moves for Taylor and Lazio centre-back Michael Ciani.
"There will always be names that will be bandied around," Hughton added. "The majority I can assure you have no substance. Some will be because of agents asking questions or putting names to us.
"I want to deal in fact and we have not made a bid for Scott Dann. Steven Taylor is one I can understand why we are being linked because of my previous connections to the player.
"Regards that one [Ciani] again, that is all part of the rumour mill. Of course we make phone calls and enquiries to see if players are available and amongst all that there is speculation. We are looking to improve the squad."