Simpson, 17, has come up through the ranks with Hartlepool, and whilst he only made his senior debut in April of this year, he is already making waves.
The striker has scored once in three games for Hartlepool this season, and his exploits for the North East side are unsurprisingly attracting interest from Premier League clubs.
The Hammers have a number of strikers at the club right now, with Javier Hernandez, Diafra Sakho and Carroll himself, but West Ham may also want to bring in a young striker to develop over the coming years.
Simpson fits the bill, and West Ham may hope that he can the next player to make the jump from non-league football to Premier League stardom, having seen the likes of Chris Smalling, Michail Antonio, Charlie Austin and Jamie Vardy make similar paths in recent years.
It's claimed that Simpson could cost West Ham just £60,000 – less than a week of Carroll's wages – and the Hammers could look to groom him as Carroll's long-term successor in attack.
With West Ham now hoping to secure a deal, the Hammers may bring in Simpson in January, and either loan him out or leave him in their development squad for the foreseeable future.