The ex-England and Blues midfielder has enjoyed mixed success as a head coach.
While his permanent stint at Chelsea did feature successes, he struggled at Everton and during his caretaker spell at the Stamford Bridge club in 2022/2023.
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Per The Mirror, Lampard is seen as an option to be Vincent Kompany's successor at Burnley.
The Clarets are also assessing former Nottingham Forest manager Steve Cooper.
Burnley were rocked by Kompany leaving for Bayern Munich, despite their relation to the Championship this season.