The Morocco international has been a regular starter for the Blues since his impressive showing at the World Cup but could still leave them before the transfer deadline.
The west London giants have had a huge spending spree of more than £150 million this month and Ziyech is one of those that could help recoup some funds.
Roma initiated their interest in Ziyech last week before Everton entered the race. It now appears the Magpies are also in the running to sign the former Ajax star.
The 29-year-old had an outstanding World Cup campaign with Morocco. He played a key role in their run to the semi-final stage before their elimination by France.
His form has been rewarded with a regular role under manager Graham Potter in recent weeks, but the board may still decide to sell him, having brought in Noni Madueke.
The Blues have signed three forwards this month – Mykhailo Mudryk, Joao Felix (on loan) and Madueke. The latter seems a direct replacement for Ziyech on the right wing.
With Raheem Sterling and Christian Pulisic due to return from injuries soon, Ziyech seems the most likely candidate to be shown the exit door before the transfer window closes.
Chelsea may prefer to offload him to either Roma or Everton rather than Newcastle. The Magpies are currently third in the league table, 10 points ahead of Chelsea in 10th.
The Blues would not want to strengthen the Magpies’ Champions League bid by handing them their player. On that basis, we won’t be surprised if Eddie Howe’s side fail to sign him.
If Ziyech were to choose between Roma and Everton, the former could be his destination.
The Toffees have just sacked Frank Lampard from the manager’s job. Ziyech may not want to join a club facing a genuine fight for survival in the Premier League this term.