Rakitic has been linked with a move away from the UEFA Europa League champions, with a host of European clubs interested in the Croatia international.
The 26-year-old's father said La Liga's top three – Real and Atletico Madrid and Barcelona – had put offers on the table for his son's services.
Castro said Sevilla were 'relaxed' about the situation and wanted to keep Rakitic, whose contract expires in June 2015.
"The last offer we made to Rakitic was a significant percentage of our total budget," Castro told Sevilla's television channel.
"We made this offer because we want him to sign.
"We want to make sure that he stays, not that he leaves. We want the team to be strong and for all Sevillistas to enjoy it.
"We won’t make anyone stay who doesn’t want to be at Sevilla. Anyone who wants to walk through the door can do it, though it has to be at our price.
"We are relaxed and we have no need to sell."
Rakitic's future is likely to be decided after the FIFA World Cup.
