Mjallby are seeking a new head coach after Kim Hellberg left for for the Middlesbrough's manager job.
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And among the candidates under consideration is Burchnall, says BBC Sport.
The 42-year-old's most recent assignment was as assistant manager to Steve McClaren with the Jamaican national team.
Burchnall has previously been manager of Östersunds FK, Notts County and Forest Green.
The Englishman has also been an assistant coach at Anderlecht and Wolverhampton.