The Spanish side's president insists they are still in negotiations with the player over a new deal, and he admits they want to ensure Unai Emery remains in charge
Banega's deal expires at the end of the season and negotiations over fresh terms have been underway for several months.
Reports in Italy have suggested the Argentina international has already agreed to join Serie A club Inter this summer, but Castro is hopeful he will stay at the Ramon Sanchez Pizjuan.
"Our negotiations continue," he said. "We wait to close an extension but we're talking about a top player who is really valued by all clubs.
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"I like that the player is working hard for us and is defending Sevilla's shirt each day."
Castro also spoke of the club's desire to keep coach Unai Emery, with Sevilla having lost just one of their last 23 games in all competitions as they bid for a top-four finish in La Liga and a hat-trick of Europa League wins.
"We didn't have a good beginning this season but we always trust on our coach," the president said.
"He is an excellent coach and my wish is that he can keep working for us for more years. I will try."