Chelsea and United were closely linked with a move for Turan before he joined Barcelona last month.
Despite being included in the squad Turan is unable to play due to the FIFA transfer ban.
Barcelona are unable to register any new players before the new year as a result of the transfer suspension.
Despite being unable to play a competitive game until January Enrique wants Turan to remain at the club and not leave on a short-term loan.
Full squad: Marc-Andre ter Stegen, Jordi Masip, Jose Suarez, Gerard Pique, Ivan Rakitic, Sergio Busquets, Pedro, Andres Iniesta, Luis Suarez, Rafinha, Marc Bartra, Douglas, Jordi Alba, Sergi Roberto, Adriano, Thomas Vermaelen, Jeremy Mathieu, Arda Turan, Aleix Vidal, Sandro, Munir, Alen Halilovic, Sergi Samper and Gerard Gumbau.