ChronicleLive says Newcastle chiefs have posted scouts to keep tabs on Garner this season.
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Everton boss David Moyes has declared Garner the best performing midfielder in the country and this form has brought him to the attention of Newcastle.
No direct contact with Everton has been established, but Garner is a target ahead of the January market.
The former Manchester United prospect is rated at £20m and his deal runs to next summer - though Everton have a 12-month option.