Spanish Publication AS says that Batshuayi remains the priority target for the La Liga side but they will turn their attention to the Liverpool striker if the Blues keep delaying the departure of the Belgium star.
Sevilla are trying to bolster their attack during the current January transfer window following a disappointing start to the season.
Batshuayi, 24, emerged as their number one target at the very beginning of the current transfer window after they made an attempt to bring the Chelsea forward to La Liga in the summer.
The 24-year-old forward has barely played under Antonio Conte during the opening half of the season and it has been said that he is also likely to make the switch to Spain in order to secure more regular time.
AS understands that the negotiations between Sevilla and Chelsea are also at an advanced stage for the player to spend the second half of the season on loan in La Liga.
However, the deal is currently on hold with Conte having asked the Blues to sign a replacement before sanctioning the departure of Alvaro Morata's current back-up.
AS claims that Sevilla are considering other alternatives as the Andalucian side need reinforcement to help new manager Vincenzo Montella to turn around their current fortunes.
Sevilla still expect Chelsea to sign a new striker to allow Batshuayi leave but the Spanish publication says that Liverpool striker Sturridge "would be their chosen one" if the Blues don't give them a response soon.
AS says that Sturridge is also keen on leaving Liverpool this month to improve his chances of playing the summer World Cup.
The Spanish publication understand that Sevilla would be keen on getting the England international on loan until the end of the current season.
It is uncertain whether Liverpool would accept such a deal with The Daily Mail recently reporting that the Merseysiders will only let him go in a permanent deal worth around £30m ($41.2m).
Jurgen Klopp refused to rule out Sturridge's departure when asked about the future of the £150,000-a-week forward last week.
"I have nothing to say about that. It's how it is. We will see. Until 31 January a lot of things can happen in the transfer window," the Liverpool said boss when asked about Sturridge. "You will probably know before I do. But I have nothing to see. We will see, not only with Daniel, we will see what can happen in the transfer window."