Heavily linked with Manchester United over the January transfer window, Moreno ultimately stayed with the Spanish giants.
Castro revealed a Premier League bid for the left-back was rejected last winter, but he said another offer this summer could be more favourably received.
That's put Liverpool on red alert, with Brendan Rodgers on the lookout for a left-back with Aly Cissokho set to return to Valencia at the end of the season after failing to win a permanent deal.
"Last December we rejected an important offer from a Premier League side for Alberto Moreno," Castro told Spanish radio station Onda Cero.
"There are many clubs tracking him weekly. In December we understood that it was not the right moment to sell him. But if we received a very good offer for him we will consider his exit.
"I believe that he is young and he is going to have a very successful career. And I hope he stays at Sevilla but if we received an amazing offer he will leave."
United were thought to be keen on Moreno earlier this season, and the 21-year-old has been scouted on several occasions. David Moyes could need a new left-back at the end of the season, as Patrice Evra is out of contract.
The Frenchman has been linked with a return to Ligue 1, and he will be available on a free transfer at the end of the current campaign.
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