The Dutch manager has won league titles in Germany, Spain and Netherlands, as well as the Champions League with Ajax, and could land a role as a sporting director at Anfield
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The club are currently searching for a successor to Kenny Dalglish, and their criteria are thought to be a young coach with title-winning experience.
They have since had approaches for Ajax's Frank de Boer, Swansea's Brendan Rodgers and Borussia Dortmund's Jurgen Klopp turned down, and major contenders for the role now seem to be Wigan manager Roberto Martinez and former Chelsea coach Andre Villas-Boas.
Van Gaal was last in management two years ago with Bayern Munich, when the Bavarians were crowned Bundesliga champions and were defeated in the Champions League final by Jose Mourinho's Inter.