According to A Spor (h/t Nihat Emre Kocaaslan of Sport Witness), an offer has already been made for the England international.
Per the report, Delph isn't the only player Besiktas are eyeing on loan, as they would also like to add Liverpool's Loris Karius after the Reds added Alisson as their No. 1 keeper during the summer.
Like Karius, Delph is seemingly expendable, as Benjamin Mendy has returned to full health and has enjoyed a phenomenal start to the season. Former Sky Blues star Paul Lake was in awe of his latest performance, a 6-1 demolition of Huddersfield:
Delph is a natural fit in the centre of the park but was a little-used bench option at the Etihad Stadium going into last season, when Mendy went down with an injury. Manager Pep Guardiola turned him into a makeshift left-back, and the former Aston Villa man impressed, surprising just about everyone.
The 28-year-old even made England's 2018 FIFA World Cup squad, with his versatility a key attribute. Comfortable in defence, his best position remains in midfield, where Besiktas would likely use him.
The Turks had to part with on-loan star Anderson Talisca, and so far, they've yet to find a quality replacement. Delph could be a great instant-impact solution, and the player himself might be keen on the move as well, given he likely won't be seeing too many minutes with City.
The Sky Blues would be unable to bring in a replacement and Guardiola may not be willing to sacrifice some of his depth, but for the right loan fee, this could be a move that goes through before the end of the summer transfer window.