Hoyle wants Town to push forward under their German head coach, and says Paterson, 24, could be part of their plans.
But he says signing Wales international midfielder Huws, 22, would be “too expensive”.
And Hoyle revealed that with Joe Murphy out for six months after shoulder surgery, Town have two new keepers “lined up”.
On former Walsall player Paterson, who has made 34 Town appearances and scored seven goals, Hoyle confirmed: “We would like to sign him.
“However at this stage, Forest are going through a sale process, so are in no man’s land regarding transfers.
“We are trying to talk to them, but any new manager might want Jamie and we are not in a transfer window in any case.
“It’s a little bit up in the air, but we do want him, and we will keep trying.”
Paterson, who cost Forest £1m in 2013 and is under contract until 2018, has previously expressed a desire to stay at Town.
Huws made his 29th Town appearance and Steer, 23, his 36th against Birmingham.
And Wolves winger Rajiv van La Parra’s loan will be made permanent in a reported £750,000 deal this summer.