Jackson, 24, has fallen down the pecking order at Chelsea following the arrivals of Liam Delap and Joao Pedro.
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The Senegal international has been linked with several Premier League clubs, along with German giants Bayern Munich along, after communicating with Chelsea that he would like to leave.
According to The Telegraph, Jackson would prefer a move to Newcastle over anyone else in the remaining few weeks of the transfer window.
Eddie Howe’s side have had some rotten luck in the transfer window so far, missing out on the likes of Pedro, Hugo Ekitete, and Benjamin Sesko.
Alexander Isak is also pushing for a move to Liverpool, meaning they will need to sign a striker this summer.