The Liga club’s director of football, Ramon Verdejo, says a bigger bid will secure the player's move to Anfield
Reds boss Brendan Rodgers looks to have identified Alberto, who scored 11 goals in 38 appearances on loan at Barcelona B last season, as an extra attacking option.
Verdejo confirmed that Liverpool have made a "very good" offer for the 20-year-old, but insisted only a higher fee will see him join the Anfield outfit.
"Liverpool's interest in Luis is real, but nothing has been signed. They've made the player a very important offer," Verdejo told Sevilla's official TV channel La Bombonera.
"I recall that much of a fuss was made when we loaned him out. As it stands, we all agree that he now has a better value in the market and has grown as a footballer.
"The offer we have on the table is a very good one with respect to where Luis is currently. We don't know what will happen in the future. To date, we haven't accepted the offer."
Luna is expected to complete a move to Villa in the near future, becoming Paul Lambert's second defensive recruit following the arrival of Jores Okore last week.
Verdejo added: "It is true that we are very close to finalising his move to Aston Villa."
Finally he stated the club will only sell Premier League targets Geoffrey Kondogbia, Ivan Rakitic and Alvaro Negredo if they receive significant offers.
He added: "We have had offers for Kondogbia, Rakitic, Medel and did not listen to them. If no significant offer comes in, we will not sell Negredo. But, do not forget who the player involved is. The figures being reported of €15-18 million are insufficient.
"[Kondogbia], his father, Doyen and Sevilla think it suits him stay in the club, he will grow and we are sure it will be worth even more next year."