Greaves was admitted to a hospital near his home in Essex on Tuesday, although he is not thought to have coronavirus nor to have suffered another stroke.
The Spurs, Chelsea and England great has been wheelchair-bound since suffering a major stroke in 2015.
Greaves' agent Terry Baker, who runs his official social media accounts, wrote on Facebook on Friday: "We have had 1000s of people enquiring after Jimmy and sending love. We thank you for that from the bottom of our hearts.
"It's still a case of no news is good news at the moment. Jimmy isn't a well man but he is in hospital receiving the best possible care thanks to the amazing doctors and nurses of the NHS at this difficult time for everyone.
"The love shown to Jim by so many 1000s of you is appreciated so much by the family and all of those close to him.
"If and when there is anything significant to report I will post again, happy Easter to everyone and Stay safe.
Earlier this week, Spurs and Chelsea icon Glenn Hoddle urged Tottenham’s greatest-ever goalscorer to “keep fighting”.
Please all say a prayer 🙏 for Jimmy Greaves a true Legend .Keep fighting Jim 😎— Glenn Hoddle (@GlennHoddle)April 8, 2020
Hoddle, who watched Greaves on the terraces as a young fan at White Hart Lane, tweeted: “Please all say a prayer for Jimmy Greaves, a true legend. Keep fighting, Jim.”
It followed Greaves' former Tottenham teammate Cliff Jones sending out similar well-wishes earlier in the week.
Jones wrote on Twitter: "Wishing my dear friend and teammate @jimmy_greaves a speedy recovery. Love from the Jones family x".