Having seen his team end 2014 with a whimper, the 55-year-old wants to use the transfer window to strengthen and reshape his squad.
So far he has added right-back Ryan Higgins and striker Cory Williams on permanent deals, and taken midfielder Josh Green on loan from Fleetwood Town and borrowed Aston Villa striker Thomas Strain.
Heading through the exit door have been Connor Roberts, John Disney and Wayne Riley, while Jamie Menagh and Liam Blake have been loaned to Marine.
Burr, whose side have struggled for goals since losing Matty Hughes and Rhys Oates, told The Chronicle he was exploring all possible options to improve his forward options.
He was priced out of a move for Michael Gash, who joined Barnet on Tuesday, and another target has attracted interest from a Premier League club.
Burr continues to keep an eye on incomings at Fleetwood Town and Barnsley with a view to re-signing Hughes or Oates, and has also been assessing a couple of trialists.
He has had more success in improving other areas of his squad with Canadian goalkeeper Jon Viscosi close to signing and has an agreement to bring in a midfielder from a League One club, which should be completed in time for the game at Southport on Saturday (3pm).
Viscosi, 23, played against the Blues pre-season for Tranmere Rovers , where he was on trial, and has been at Brackley Town, Carlton Town and Tiverton Town.
Burr said: "I'm taking a midfielder from a League One club and and we've had a keeper in, Jon Viscosi, who we're looking to sign as a replacement for Connor, who has signed for Bangor.
"I'm still looking obviously at the striking area. I've made I can't remember how many phone calls over the last couple of weeks chasing players and there's one or two that I was hoping for where it's sort of fallen through for one reason or another.
"What I don't want to be doing is going in, panicking and bringing in somebody just for the sake of it. I want to try and make sure they are the right type and they can handle this division.
"It's not easy sometimes because the striking position is an important area but since we lost Matty and Rhys it's an area that we need to strengthen.
"I was hopeful of getting a lad from a League Two club on loan and all of a sudden there's a Premier League club who've come in for him who want to buy him so that's good for the lad but disappointing for us because I thought we were close to getting him.
"It's one of them at the minute where we're still looking around and we've had one or two in on trial.
"There's a lot of player out there available but we've generated a bit of money from the cup that's there to use and with the likes of Jamie and Wayne going, we've managed to do a deal with John Disney on his contract so he's going to be leaving as well and that's released a little bit of money too.
"We're working pretty much around the clock at the minute because we want to kick on in January."
Chester have recorded just one win in five league games since beating AFC Telford United 2-0 at the start of December.
Disappointing defeats to Altrincham, twice, and Braintree Town have seen them drop from the edge of the top half to 17th in the table.
Burr said: "I'm really disappointed with how the Christmas period went with results against clubs that I feel that if we'd have hit the form we had leading up to the cup run then we wouldn't have had a problem against those teams.
"I've said all along that we've got a squad of players here that it's going to fluctuate in certain performances but it's sometimes hard to get your heard around it when you can see how good they've been to how poor they can be
"One or two have lost their confidence a little bit, one or two have dipped with their performances and what have you so with all them sort of things we need to get back on track."