Goal understands that Morata's representative, Juanma Lopez, met with the Liga club recently in a bid to earn his client a move back to his homeland.
Sevilla are willing to pay the entirety of Morata's £140,000-a-week wages to bring him to Andalusia as they aim to continue their unlikely title bid.
Chelsea are unwilling to let him leave Stamford Bridge unless they can secure a replacement themselves during the January window.
Morata signed for the Blues from Real Madrid in a deal worth an initial £58 million in the summer of 2017, but the 25-year-old has struggled for consistency in front of goal.
In total he has scored 24 goals in 72 appearances for the west London outfit - nine of those goals coming this season - with his place in Maurizio Sarri's side far from assured.
Eden Hazard has been prefered to him in recent weeks as Sarri introduced a false nine into his formation while Olivier Giroud has also provided competition for Morata over the last 12 months.
"It is more important to score than celebrate. He scored two goals in the last match, in the season he has nine.
"In his best season at Madrid he scored 20 goals, so he will be able to have a very good second part of the season and he will try to reach his best."
Quite where Morata would fit into the pecking order at Sevilla is unknown, with Wissam Ben Yedder and Andre Silva having netted 24 goals between them in all competitions this season.
The latter's form, however, has dropped off in recent weeks after a fast start following his loan arrival from AC Milan, and with Luis Muriel having left for Fiorentina already in the winter window, Morata could yet earn a starting berth should he move to the Sanchez Pizjuan Stadium.
Chelsea's search for a replacement will not see them resurrect their interest in Milan's Gonzalo Higuain, with the Blues deciding against pursuing the deal after it was deemed too complicated by the club's hierarchy.
Bournemouth's top scorer Callum Wilson is an option , though the Cherries are understood to be standing firm in not selling the England international.
And with more than three weeks of the window still left and a number of possibilities still to emerge, Morata could yet be made to wait before finding out his fate over the next month.
Additional reporting by Paco Rico and Romeo Agresti.