The forward moved to Anfield from Celta Vigo in June last year after a return of 35 goals in his previous 69 La Liga games caught the eye of manager Brendan Rodgers.
In the absence of suspended striker Luis Suarez, Aspas featured in Liverpool's first five Premier League matches but struggled for starts thereafter, with his only goal coming against Oldham Athletic in the FA Cup.
His Liverpool future has been cast into doubt in the close-season and Emery revealed that he had been monitoring the situation with the intention of securing the 26-year-old's services.
"He is a player who burst onto the scene with two very good years," Emery told Estadio Deportivo. "He moved to England but has not been involved there.
"He has some good qualities and the ability to play at a high level. He fits the profile but it is not easy to negotiate with Liverpool.
"But he is one of the players it would be good if we can get."
Emery also hinted at the arrival of goalkeeping support for Beto, with Las Palmas' Mariano Barbosa someone he is interested in.
"Barbosa is one of the goalkeepers we have seen and that fits our needs," he added. "We wanted a goalie to give us more height and to play with the feet, Barbosa could do that."
