The Yellow Canaries reportedly submitted a loan offer to bring in the Reds forward but the bid was rejected.
The Istanbul giants did however, end up signing another Liverpool player. Lazar Markovic joined the Canaries on a one-year loan and provided his first assist in his first start yesterday in the 2-1 victory over Bursaspor.
Origi has struggled for playing time since joining the Reds on a £10million transfer in 2014.
The young striker was loaned out to Lille last campaign but the Ligue 1 side was voted the worst team of the season according to FOX Sport.
Rodgers decided to keep Origi at Liverpool this season but also signed Ings, Benteke, and Firmino, which which pushed the Belgium international down the pecking order.
Fenerbahçe are currently first in the Turkish Super League with 13 points after five games.