The Senegal international is currently on-loan at Bayern Munich this season.
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Sport1 says Bayern have decided against pursuing a permanent deal for Jackson.
Instead, a move to Tottenham could be on.
However, there is competition for the player's signature, as Atlético Madrid is also showing interest in signing Jackson for next season.
In recent months, the striker has also been linked with Aston Villa and Napoli.
Jackson's contract with Chelsea runs until the summer of 2033.