The Chelsea striker has been linked with a host of clubs following a successful loan spell in the Championship last season with Bristol City, where he managed to bag 23 goals.
Newcastle were overly reliant on Dwight Gayle last season and the potential addition of Abraham would represent an exciting addition.
Abraham worked with Paul Clement when the Swans manager was a coach at Stamford Bridge. [Manager] Paul Clement knows him from Chelsea.
"He's a young and up and coming player we are interested in", said Jenkins. His Premier League career was cut short by the arrival of Llorente and Borja Baston last season.
It is said that Newcastle were the frontrunners for his signature with talks between Chelsea and Rafa Benitez being held this month.
"We aren't putting figures on our players".
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