The 24-year-old is expected to leave Stamford Bridge this summer following the arrivals of Liam Delap and Joao Pedro earlier in the transfer window.
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Jackson has been linked with several top clubs, including Newcastle, who are preparing for life without talisman Alexander Isak.
According to iNews, Jackson is one of several names on their shortlist, which consists of him, Yoane Wissa, Ollie Watkins and Samu Aghehowa.
It’s understood that Newcastle are hoping to sign more than one striker before the end of the window, and Chelsea, who aren’t in a rush to sell, value Jackson at around £80m.