A report from ESPN says the Blues will let Batshuayi, 24, leave the club if they can bring in a replacement striker, with West Ham's Andy Carroll and Arsenal's Alexis Sanchez among the names linked with a move to Stamford Bridge.
Sources close to Sevilla told ESPN that the club are interested in signing the Belgium international, who has only started two league games for the Blues this season.
Chelsea manager Antonio Conte is keen to strengthen his attack as he does not trust Michy Batshuayi to provide capable back-up to Alvaro Morata.
Conte opened the door for the likes of Michy Batshuayi and David Luiz to leave Chelsea in the January transfer window, saying he would not stand in the way of players looking to secure greater playing time elsewhere during a World Cup year.
"I prefer to have players who are very happy to stay here than to have players that are unhappy, because when you are unhappy you transfer this to the other players, to me, to my staff," Conte was reported as saying by ESPN on 2 January. "I don't like this. If we can avoid this I'd like to avoid this situation."
Conte is also reported to be keen on signing Red Star Belgrade's Richmond Boakye and Crystal Palace's Christian Benteke, although Carroll, 29, is seen as the most attainable before the January transfer window closes.
Chelsea have emerged as late contenders for the signing of Sanchez, after Manchester City cooled their interest over Arsenal's demand for a £35m ($48m) transfer fee.
However, Manchester United remain the favourites to land the Chilean forward, with reports suggesting that the Old Trafford club are willing to meet his wage demands of £350,000 a week.
Chelsea have played out three successive goalless draws – against Norwich, Arsenal and Leicester, respectively – and are on a four-game winless run in all competitions.