Chelsea and Liverpool, along with Paris Saint-Germain, have a long standing interest in United States international Pulisic, whose contract is due to expire in 2020.
Dortmund are adamant the forward will not leave in January, but are prepared to negotiate a transfer for the summer if they receive a big enough bid.
Chelsea would have to smash their record transfer, which stands at £57m for Alvaro Morata, to secure an agreement for the summer over Pulisic.
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