Reds chief executive Ian Ayre is in Spain in a bid to finalize a deal for the 22-year-old, and is also confident of tying up a loan deal with Atletico Madrid for Javier Manquillo.
MORE: Biggest summer transfers | Soccer's beautiful fans
Goal reported in June that Sevilla was holding out for around €23 million for Moreno, amid reports that he had already agreed terms with the Reds.
But talks are progressing after a two-month delay and Brendan Rodgers is now confident that a deal can be agreed for the Spain Under-21 international.
A agreement with La Liga champion Atletico for right back Manquillo is also close. The 20-year-old has made only six appearances in the Primera Division and would provide cover for Glen Johnson at Anfield.
The two moves would push Liverpool's summer spending past the €125 million mark following the £70 million sale of Luis Suarez to Barcelona.
Southamption trio Adam Lallana, Dejan Lovren and Rickie Lambert have all moved to Merseyside, while Emre Can joined from Bayer Leverkusen and Lazar Markovic has been recruited from Benfica.
Rogders has also signed Divock Origi from Lille, but the Belgium striker will return to the Stade Pierre-Mauroy on loan for the 2014-15 campaign.