What is the alternative to Calypso's offer to Odysseus in order to keep him on the island?

At Athena's insistence, Zeus sends Hermes to tell Calypso that she must release Odysseus, her seven-years prisoner and lover.  Calypso is undeniably upset by this news, especially in regard to the double standard she identifies among the gods and goddesses.  Gods routinely take mortal female lovers without incident, but whenever a goddess takes a mortal male lover, the gods order that he be killed in some tragic fashion.  It isn't fair.
However, she tells Odysseus that she will release him, giving him all the help he needs to build a sailing vessel and any provisions he requires for his journey.  She will not disobey Zeus.  She isn't happy about it, though, and she offers Odysseus immortality should he decide to remain with her.  Calypso also knows how hard Odysseus's journey home will be, and she advises him to remain in ease and comfort on her island.  His choice, then, is to remain in safety, immortal, and beloved by a goddess or leave and eventually reach home after a great deal of personal hardship.