Both players are out of contract in the summer.
Midfielder Hunt, aged 21, spent the first half of the season on loan at National League side Grimsby Town but has been recalled with several League 2 clubs interested in his services for the remainder of the campaign.
Central defender Brennan, also 21, was recalled from a loan spell at Notts County, also of the National League, in October amid an injury crisis in the Owls’ defence and has since made nine appearances for Wednesday.
Asked if there had been any developments regarding a new deal for Hunt, Moore replied: “We are just in the process of that now.
"Steps and measures have been made towards that.”
On Brennan, Moore added: "Like Alex Hunt we are in the process and talking.
“That’s already advanced talks. It’s well and truly down the road already with him, which is great.
"We’ll see how the next few days go.
"Ciaran’s another youngster that we feel has the right potential and when called upon he’s stepped in and done really well.
"He’s another youngster that has parts of his game to develop and we will continue to develop them.
"He’s developing nicely, he’s got a lovely maturity about him for someone so young and we’ll keep working with him and make sure he’s doing the right type of work to see him get better.
"It’s great for him that he’s competing against some seniors in terms of where his performances have been of late.”