While nothing formal has been established with Chelsea, United have spoken with the striker's agents to register their interest.
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BBC Sport says United officials met with agent Ali Barat to confirm their interest.
Jackson is on a shortlist of striker names for United, which have also been linked with Sporting CP centre-forward Viktor Gyokeres again as talks with Arsenal drag on.
Jackson's future at Chelsea is in doubt after the arrival for Liam Delap and Joao Pedro this summer.