Sevilla sporting director Ramon Rodriquez revealed Celtic had made the loan offer.
"Our answer was negative as Hinkel will only leave the club in a sale," he told the Scottish Sun. "We want to receive bids for him and if that happens there could still be movement."
Hinkel's agent has claimed at least three clubs are trying to sign him, with Wolfsburg reportedly keen to take him back to Germany.
But the player has described Parkhead as the ideal destination.
"I came here to play but that has become impossible because Daniel Alves is in my position," said the 25-year-old former Stuttgart player. "I have told the club that I'd like to move and, of course, Celtic would be perfect for me.
"It is a club with great history and they are in the last 16 of the Champions League again.
"I haven't spoken to anyone from Celtic yet but I know the position and it would be a favourable move for me."