The Evening Standard have reported that Chelsea have pulled out of the race to sign QPR striker Charlie Adam and therefore will not sell Remy this summer.
Remy’s future at Stamford Bridge was cast under doubt when Chelsea signed Radamel Falcao on loan from Monaco.
The France international has stated that he is happy to stay at Chelsea despite being their third choice striker.
“There are many reasons I want to stay but we won two titles (Premier League and Capital One Cup) last season and I am sure we are going to win more next season.
“So for me it’s really exciting to be a part of this project. There is no reason for me to leave.”
Besiktas have been closely linked with the 28-year-old over the past month.
The Black Eagles are in the market for a striker after Chinese giants Shanghai Shenhua snapped up Demba Ba for €14 million.
Remy – who has three years remaining on this contact with the Blues – provided two assists and scored nine goals in 29 appearances in all competitions for Chelsea last season.