The Toffees may have splashed the cash on signings like Jordan Pickford, Michael Keane and Gylfi Sigurdsson over the summer, but many are putting their early-season struggles down to the lack of a top striker.
Everton sold top goalscorer Romelu Lukaku to Manchester United in a big-money deal this summer, and whilst Sandro Ramirez arrived from Malaga in a bargain move, the Toffees failed to sign a real replacement for Lukaku.
Goals have been hard to come by as a result, and The Sun now report that Everton are plotting a £20million move to sign West Ham United striker Andy Carroll in the January transfer window.
Carroll, 28, has battled a host of injury blows during his time with West Ham, but he has hit 30 goals in 114 games for the Hammers since joining from Liverpool in 2012.
Carroll's time at Liverpool was a complete disaster, but with just over 18 months left on his West Ham contract, Everton could launch a shock move to bring him back to Merseyside.
On the face of it, this rumour seems odd; Carroll's injury history is well-documented, and he hasn't hit double figures in goals in the Premier League since the 2010/11 campaign.
However, Koeman has a penchant for pursuing or working with target man, having enjoyed great success with Graziano Pelle at both Feyenoord and Southampton.
Carroll fits the bill, with similar strength and aerial prowess, meaning Koeman's alleged interest may make some sense – but whether Everton fans would support the move is another matter.