The English champions are said to be keen on the América de Quito midfielder, but City would struggle to obtain a work permit for the 20-year-old, as he is not yet a full-time international.
The rules on work permits in Scotland are considered to be more relaxed. Cifuentes would likely get more first-team football at Celtic, and is understood to be interested in a move to Scottish football.
Cifuentes was part of the Ecuador squad that finished third in the recent Under-20 World Cup, and his performances are believed to have caught the eye of clubs in Germany and Italy, as well as Celtic and City.
The Hoops are on the hunt for midfield reinforcements, after missing out on David Turnbull and with Olivier Ntcham's future still uncertain. The likes of Kundai Benyu and Eboue Kouassi also seem out of the picture at Parkhead, while Nir Bitton has been deployed as an auxiliary centre-back in recent matches and could continue there for the foreseeable.
Cifuentes operates as a defensive midfielder, but likes to get forward. His physical strength and tidiness on the ball make him an attractive proposition for clubs looking to upgrade.
He is still young and not the finished article however, with the right coaching, he could be moulded into a key player if he makes the move to Europe.