The England international is struggling to cement a regular spot in the first team, having started just four Premier League games this season.
The Hammers are believed to be interested in swooping for the striker as they are in need of firepower, having scored just 14 goals in 13 Premier League games this season.
However, according to The Mirror, Klopp will not entertain the idea of selling Sturridge in January, nor will he allow any of his players - apart from Mamadou Sakho - to leave in the next transfer window.
Liverpool will be without Coutinho during the busy festive period due to an ankle injury, while Mane will be absent in January as he represents Senegal in the Africa Cup of Nations.
As two of Klopp's attacking stars will be unavailable, Sturridge is likely to get some game time, and it is believed that because of that reason the 27-year-old will not force a move away next month.