Burnett, formerly first-team coach at Victoria Road, was handed the reins on an interim basis in late February after John Still opted to swap the Daggers for non-league Luton, ending his nine-year tenure with Dagenham 16th in League Two and eight points off the drop zone.
Burnett recorded two wins, four draws and six defeats in his 12 games at the helm, narrowly avoiding a bottom two finish merely on goal difference despite Saturday's final-day 1-0 loss at home to York as fellow strugglers Barnet also went down 2-0 at Northampton.
And the 41-year-old now wants to hold talks with the powers that be at Dagenham in a bid to land the job full-time.
"Everyone has been really supportive and the board have been brilliant," Burnett told BBC London 94.9. "We'll sit down and hopefully have a chat and see where we go from there.
"I have made it quite open and hopefully I will be here next year and we can do better than we have done in the last two seasons.
"Pre-season has been scheduled already and we'll be looking to bring one or two in.
"If it all works out like we hope for next season we might see a slightly different way of doing things."
Meanwhile, Daggers defender Luke Wilkinson scooped the club's Player of the Year award ahead of second-placed Femi Ilesanmi and Scott Doe, in third.