The Europa League champions have put the Liverpool duo on their shortlist.
Both players have been linked with exits from Anfield this summer, with neither said to be in manager Jurgen Klopp’s long-term plans.
Allen found himself slipping down the pecking order last season as the German preferred James Milner, Emre Can and Jordan Henderson in the centre of midfield.
He has starred for Wales at Euro 2016 though, and several clubs are thought to be interested in his services as a result.
Alberto meanwhile has spent the last two seasons out on loan, first with Malaga and then Deportivo La Coruna.
Sevilla have been linked with both players, and Sporting Director Monchi has confirmed they are on a list of potential targets.
“It will take all afternoon to name everyone and I don’t like talking about players who aren’t Sevilla’s,” the Mirror quotes him saying.
“Ganso and Allen aren’t the only ones on the list. Luis Alberto? There’s an offer and we’re evaluating it. Negotiations haven’t started. We’re considering other names.”
It now remains to be seen whether the Europa League champions will make a move for either player this summer.
Liverpool have set relatively big asking prices for the duo, with the Mirror report claiming they want £7 million for Alberto and £10 million for Allen.
The quoted price for the Welshman is lower than previous reports of £14 million, which Estadio Deportivo had reported was too big a price for Sevilla to pay.