The striker has been put up for sale by Chelsea at a starting price of £60m.
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The Mirror says Chelsea have hawked Jackson across the Premier League - with Newcastle, Aston Villa, Manchester United and Arsenal all offered the centre-forward.
Chelsea are eager to make the sale in order to raise funds and make room in their wage budget to bring in late additions to manager Enzo Maresca's squad.
Maresca has particularly demanded a new centre-half be added before the market shuts after the knee injury suffered by Levi Colwill last week.