The Fiorentina striker has netted six times in 14 matches for La Viola in Seria A this season, and the Premier League pair have been impressed by his performances.
Babacar’s power and pace has proven a threat to defences in Italy, and he looks a good fit for England’s top tier.
Babacar has been a key player for Fiorentina this season, but if there is any potential to do a deal - both Leicester and Palace are keen to make them an offer.
Leicester have made a wonderful start to their Premier League season, and are competing for a top four places, but Claudio Ranieri doesn’t want his side to rest on their laurels.
The experienced manager is keen to strengthen in January, and finding another attacking option could be important.
Palace, meanwhile, have failed to find a potent goalscorer so far this term - but Alan Pardew reportedly believes Babacar could fill this void in his squad.