The People says Laudrup is expected to leave the Liberty Stadium at the end of the season - so Swans chairman Huw Jenkins has been plotting his next step.
Jones, 43, is Roberto Martinez's assistant at Everton, and also worked under him at Swansea and Wigan.
He was lined up as Brendan Rodgers' replacement at Swansea in 2012 but did not feel ready. But it is understood he would now feel more prepared.
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