Per the source, talks have reached an advanced stage and the Black Eagles are on the verge of completing the loan deal.
The transfer has however, yet to be finalised and Orman will enter the final round of negotiations with City and Nasri.
City reportedly want Besiktas to cover his wages in full but the Istanbul giants want to negotiate a deal which would see the Premier League giants cover part of the salary.
The France international has fallen out of favour with City boss Pep Guardiola and told he can leave the club in pursuit of first team football.
Besiktas would be able to offer him just that in addition to Champions League action this season after winning the 2015-16 league title.
Nasri has won two Premier League titles and had established himself as a star player at City until the appointment of Pep Guardiola.
The 29-year-old would be joining Marcelo from Barcelona and Benfica starlet Anderson Talisca as the Eagles third high profile transfer if he were to make the move this summer.