The IFK Norkopping striker has been scoring goals for fun.
The striker is said to have caught the attention of both clubs, as reported by The Sun, and relayed by Sky Sports.
West Brom and Palace are two teas always looking for a bargain and Kujovic would certainly not command a hefty price-tag.
He is out of contract this year and that means his current club IFK Norkopping are resigned to losing him in the coming months.
West Brom and Palace would be getting their hands on a player who has been having quite the impact in Swedish football.
Kujovic, who was born in Montenegro, joined Norkopping from Turkish side Kayserispor in 2013. The 27-year-old has since gone on to score 34 goals in 59 games for the side - as they won the Allsvenskan in 2015.
His impressive form in the domestic game has even seen him earn his first Sweden cap this year. He featured for Sweden against Estonia and Finland in January, opening his account for his nation in a 3-0 win against the Finns.