Badashile was already on the radar of the Magpies in the January transfer window but along with a number of other centre-back targets he escaped their grasp.
The centre-back stayed on at AS Monaco and there has continued his performances that have seen him become an in-demand defender.
Newcastle are joined by the Hammers in their pursuit of Badiashile, while Italian giants Juventus also keen on the centre-back.
The Magpies though are hoping they are able to recruit the centre-back in the summer, according to French outlet Foot Mercato.
Badiashile is expected to cost around €40M in the summer and the centre-back has a contract at the Ligue 1 club that stretches until the end of the 2023/24 season.
The Magpies are still pursuing other January centre-back targets like Sven Botman and Diego Carlos, but the former is close to a move to AC Milan.
Badiashile has made 19 league appearances this term, missing many games due to injury, including one picked up in the January window, and was part of a defence that kept a clean sheet against Paris Saint-Germain last month.
