The La Liga side have provisionally agreed a €1.5m loan fee, and are also willing to pay a significant portion of his wages.
Sevilla are also looking at alternative options like Everton's Sandro Ramírez and are even interested in Daniel Sturridge, but they are thought to prefer getting the Belgium international in through the door.
Chelsea, however, will not let the Belgium international go until they are certain of landing a forward in the current window.
The Blues are in turn trying to secure Carroll, but any deal will have to be on a permanent basis after West Ham refused to countenance a loan switch.
The 29-year-old has emerged as a target to give Chelsea more depth at centre-forward, the club having missed out on the season's first choice Fernando Llorente in a summer transfer deadline day battle with Tottenham.
Carroll was left out of West Ham's FA Cup third round replay match with Shrewsbury, while Batshuayi is expected to start Chelsea's game against Norwich on Wednesday.