The Portuguese star had agreed terms on a move to Liverpool before Real scuppered the deal by demanding a £2million fee, while Inter Milan are keeping an eye on proceedings.
"It's a situation that is up in the air," said Real Madrid vice-president Emilio Butragueno.
"Luis is an extraordinary professional and we have a very good relationship with him.
"He didn't play much last season but he is a winner, he wants to play.
"We hope that we reach an agreement that satisfies both sides."