Chelsea starlet Tammy Abraham has scored 26 goals for Bristol City
The towering 19-year-old has impressed with the Robins after bagging 26 goals in all competitions.
Abrahams is unlikely to have a future at Stamford Bridge, though, considering £30 million young striker Michy Batshuayi has barely had a look in under Antonio Conte on their way to the Premier League title this season.
Chelsea manager Antonio Conte and Michy Batshuayi
The Hammers were turned down by Batshuayi last summer and Bilic has been heavily linked with a renewed bid for the Belgian this summer.
But it could prove better business to make a move for Abrahams instead with staying in London likely to appeal to the player rather than uprooting for a move to Goodison Park.
Everton manager Ronald Koeman with West Ham United boss Slaven Bilic
It could be argued West Ham's need for a striker is more acute given their reliance on injury-prone duo Andy Carroll and Diafra Sakho.
But should - as is expected - Everton lose Lukaku this summer they too will be left massively short of quality up front.