The Light Blues boss is keen to bolster his squad in the January transfer window and after the win over Dundee United at Tannadice last Sunday he spoke in glowing terms about Cantwell and Davies, both of whom have been linked with a move to Ibrox.
Ahead of the Viaplay Cup semi-final against Aberdeen at Hampden Park on Sunday, with striker Antonio Colak and midfielder James Sands doubts, Beale updated the club's transfer situation.
The former QPR boss said: "It has progressed well. I am pleased with where it's at.
"As soon as there is news obviously we will let everyone know. We are eager to let everyone know but these things take a little bit of time.
"My bit is done, if that makes sense and now it is over to the other people to finalise things.
"But as far as I can see I am really pleased with the way two or three things are going, they are heading in the right direction.
"I didn't think anyone would be in before this game and I didn't really want to disrupt the group either.
"Hopefully in the next week or so we will see one or two things being confirmed.
"It could be up to three or four, it could be one or two.
"They have got to be the right people. There have been meetings going on. It is positive. These things are never as fast as the fans want.
"The window opens and the fans want the guy there the minute it does, it doesn't always work like that but I am positive."
Canaries boss David Wagner reportedly stated that Cantwell is not part of his plans and is talking with other clubs.
Beale said: "He's a player with a lot of ability and there will be a lot of interest in him.
"He's a player I like a lot. I said last week that out of respect that I can't really say much more than that.
"I think you are not far off the track, what you (media) are all insinuating."
Beale revealed his plans to give goalkeeper Robby McCrorie some game time before the end of the season.
Jon McLaughlin replaced veteran Allan McGregor for last weekend's cinch Premiership game against Dundee United at Tannadice and Beale will have to choose between the two for Hampden Park.
McCrorie, who in October signed a new deal that takes him to 2025, last played for the Rangers first team in August 2021 where he helped the Light Blues to a 1-0 win over Old Firm rivals Celtic at Ibrox.
Beale said: "He's got an ankle ligament injury so he's been out for two weeks and will be out for another two or three.
"He's not been in contention unfortunately but Robby is a guy I've got a lot of faith in.
"He's a young goalkeeper that needs an opportunity. He's shown he can play in our top division on loan and do well.
"He's broken into the Scottish squad as well. You go off what you see in training and I have no bias towards anyone here.
"You earn the shirt in training. I felt it was the right game for Jon (against United) because I expected the game to go a certain way.
"It didn't go that way but we got the clean sheet so no harm done.
"Once Robby is fit, the plan before the end of the season is to give him an opportunity to showcase that he can be the number one here for Rangers going forward."