The Bulldogs have made their interest in the 20-year-old known, with plans in place to lure the halfback from the Panthers a year prior to the end of his contract.
The Panthers have hinted they would be prepared to move Burton into the centres or back row to keep him on their roster, with the club also aiming to re-sign Stephen Crichton and Isaah Yeo.
Speaking to The Sydney Morning Herald, Barrett said Burton would be a sensational addition to his side.
“We’d love Matt on board here next year,” he said.
“He’s only a young player but he’s someone with a lot of ability and whose pathway is a bit blocked at Penrith.
“He’d certainly be handy. He needs to decide where he wants to be in 2022 and 2023 first.
“We’ve got two spots left. There will be a lot of moving parts in regards to recruitment.
“I’m looking forward to seeing what we have here. There are some players I don’t know a lot about, and because there was no Canterbury Cup this year there are players who haven’t played a lot of footy.”
Speaking on Flanagan, Barrett stated his excitement to be able to work with such an exciting playmaker.
“Kyle is very important for us, he’s a very good young player and someone we can build our team around for a long time,” Barrett said.
“I’m very excited to get hold of him. The skill set is there and he ticks a lot of boxes.
“He’s calm, a good kicker of the ball and a good organiser. He walked into a premiership team stuck between two internationals in Luke Keary and James Tedesco. It was never going to be easy for him but he did a great job and we’re lucky to have him.”