The pair were also teammates as players with the Cherries.
And several reports south of the border state that the duo will reunite at Liverpool, with Burchill supporting head of recruitment Dave Fallows and chief scout Barry Hunter.
The former Scotland striker, who won the Challenge Cup during a brief spell in charge of Livingston, represented the likes of Celtic, Birmingham, Kilmarnock and Hearts during his playing career, as well as a stint in Cyprus.
Burchill joined Dundee on loan from Portsmouth in January 2003 and played 15 times for the Dens Park club, including a starting berth in the Scottish Cup final defeat against Rangers.
A roller-coaster period saw him play in another Scottish Cup final in 2007 – again on the losing side, this time to Celtic – and suffer relegation in the same season.
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Former Dundee and Dunfermline striker set for key role in Liverpool backroom revolution
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