Solomon Kvirkvelia of FC Lokomotiv Moscow
It is claimed all three sides are keen to land the Georgia international ahead of Thursday's transfer deadline.
Leicester are said to face competition from Arsenal and Manchester City in their pursuit of West Brom's Jonny Evans, for whom the Baggies would need a replacement, while Palace's efforts to re-sign Liverpool's Mamadou Sakho appear to be proving unsuccessful.
Jonny Evans of West Bromwich Albion
Kvirkvelia has therefore emerged as a target for the trio, according to the report, having impressed in his nine outings for Lokomotiv Moscow this season.
The 25-year-old, who stands at almost 6ft 6ins tall, only signed a permanent deal in the Russian capital at the start of last month, having spent last season on loan there from Rubin Kazan.
Solomon Kvirkvelia of FC Lokomotiv Moscow (right)
Nevertheless, it is claimed he would 'jump at the opportunity to move to England'.
Would Kvirkvelia be a good signing for Leicester City / Crystal Palace / West Bromwich Albion?