The 30-year-old winger, who has not featured for the Toffees since February 21, was taken to hospital on Sunday with the club later confirming he is currently receiving treatment for a stress-related illness.
A short statement read: "Aaron Lennon is currently receiving care and treatment for a stress-related illness. The club is supporting him through this and his family has appealed for privacy at this time."
Greater Manchester Police said: "Police were called at around 4.35pm to reports of a concern for the welfare of a man on Eccles Old Road.
"Officers attended and a 30-year-old man was detained under Section 136 of the Mental Health Act and was taken to hospital for assessment."
A number of high-profile names have come out to publicly offer their support for Lennon.
Former PFA chairman Clarke Carlisle, who himself battled mental health problems, said: "Love and blessings to my old teammate Aaron Lennon. Nail this now and there's plenty more left in the tank my friend."
Gary Lineker tweeted: "Wish @AaronLennon12 all the very best and hope he gets well soon." Stan Collymore added: "Thoughts and love with Aaron Lennon and his family right now. I know that place, and I know he'll be fine with good support from us all."
Frank Bruno tweeted: "Thoughts are with Aaron Lennon today, stay strong & as positive as possible, there is light at the end of tunnel u will get through this boss," with former England cricketer Andrew Flintoff adding: "Lots of love and wishes @AaronLennon12 another cruel example of how mental illness can effect anybody, get well soon."
Lennon's representative, Base Soccer Agency, tweeted: "Everyone at Base Soccer sends their support to AaronLennon12 - get well soon and stay strong."