The Blue Square Premier Bluebirds have made a new striker, along with a central defender and central midfielder, their priority.
Bayliss told BBC Radio Cumbria: "It's really moving on our three main targets. Again, it takes patience.
"We've spoken to a [midfielder] who's back from America on Friday and he'll give us an answer."
Bayliss has also revealed he has opened talks with two other players over the last few days.
"We've been really busy," he said. "We met a centre-half today and myself, Darren (Sheridan) and the chairman met a centre-forward last week so things will hopefully fall-in around those three players."
The Bluebirds have made just one new signing so far this summer with the capture of Simon Spender from Wrexham.
"I've not seen a lot of movement around the clubs this summer apart from Oxford," Bayliss said.
"It is moving slowly but it is a big market out there. We could have rushed out and got five or six players in straight away but it wasn't the right thing to do.
"Slowly but surely it's coming together. We're getting answers from lads this week so it is going forward."
Bayliss said the fact that most players were contracted until the end of June meant that the lack of activity in recent weeks was always likely.
"The players themselves are also taking their time to look around," he told BBC Radio Cumbria's Matchnight programme.
"I've seen it with Carlisle, some of their players are waiting a few weeks to see what comes up and it's no different for us."
The Bluebirds also intend to use their pre-season itinerary to have a look at potential signings.
"These lads are good players and we just want to make sure that they are fit and up-to-scratch to play for us," Bayliss said.
"Some of them will excite the fans.
"We'll bring them in, have a look at them in some games and see what they think of us as well.
"As I've said before, the squad we're getting together for next season will be a hell of a lot stronger than we had last season."
Bayliss also revealed that the club are hoping to add further games to their summer itinerary in preparation for the new Blue Square Premier season.
"We've just agreed with one Premier League team to play us. Now we just need to be given a date," he said.
"We're also hoping to get another two other really good teams to come to Barrow as well."
Barrow will open their pre-season campaign against a Furness Select side at Holker Street on 11 July before a trip to Lancaster City three days later.
Championship side Doncaster Rovers will provide the opposition in Cumbria on 18 July with further games scheduled against Penrith (21 July), Witton Albion (23 July) and Morecambe (1 August).
Source: BBC Sport
Source: BBC Sport