Sky Sports understands a number of clubs are tracking highly-rated Carlisle United midfielder Brad Potts.
Sheffield United are planning to send Andy Butler back out on loan after seeing an agreement with Walsall collapse.
The former Motherwell and Inverness boss is the sixth manager in seven years to sit in the Easter Road hotseat.
Since Tony Mowbray left for West Brom in October 2006, no manager has left the role on a high.
John Collins won the League Cup but left following the breakdown of his relationship with chairman Rod Petrie; Mixu Pattelainen sealed two sixth-placed finishes but that was not deemed good enough; John Hughes was sacked months after leading Hibs into Eurpoe; Colin Calderwood could not halt a slide; and Pat Fenlon quit following protests over another derby defeat.
Butcher saw the scale of his task on Saturday when Inverness inflicted Hibs' fourth consecutive defeat 24 hours after he had said his farewells to the Caley Thistle players.
But the former England captain is not one to shirk a challenge and he left the second-placed side along with assistant Maurice Malpas in a bid to rouse Hibs and unleash their potential.
"There are some good players there, players whose confidence is rock-bottom at the moment," Butcher said.
"After Saturday's performance, I think the only way is up. It has to get better and it will get better.
"That comes from an understanding from the players in ourselves, trust as well, but that will come.
"It's a great challenge and I'm really looking forward to it. It's exciting.
"It's like I'm looking down a tunnel and everything is rushing towards me.
"It's like everything is hitting me at the moment, which is brilliant. That's what you want. That's exciting. "That's frightening but exciting too."
Butcher's chief scout at Inverness, Steve Marsella, is set to join him at Easter Road after helping him take the likes of Northern Ireland striker Billy McKay from lower-league football in England to the Highlands.
But Butcher will give the current Hibs players the chance to prove themselves.
"Everyone has talked to me about January and can you get players in and that sort of thing," he said.
"That's a little bit disrespectful to the players here.
"The players here can have a bearing on that. If they play very well and play to their potential, then there will be a few less players coming in than we normally do."
Butcher, who was at training on Tuesday morning, added: "It's up to the players but I'm very confident they will respond. They have already shown that.
"They are a great group of lads and we want to get that spirit even better. That comes through winning football matches and playing well and knowing what they have to do.
"A lot of passion and commitment is what we require. The fans certainly do that. I want to make Hibs fans proud of their team."