Former England striker Greaves, who suffered a stroke which left him wheelchair bound in 2015, was admitted to a Cheltenham hospital on Tuesday - though his condition is not related to his previous illness.
Terry Baker, Greaves's agent who runs his social media channels and has been providing updates, added that the 80-year-old will undergo tests today and that "no news is good news".
Greaves has also been able to speak to his wife, Irene, over the phone from hospital.
"I did promise a statement mid morning today when I posted a statement last night," Baker posted on the former Chelsea man's official Facebook page.
"All I can say is no news is good news at the moment. Jimmy has spoken to Irene by phone.
"During the course of the day he will be having tests and when we find out the results I will post them on here.
"So watch this space and have a good thought for Jimmy as you go about your current daily routine.
"His problem isn’t coronavirus related and doesn’t seem to be related to his previous illness. Hopefully he won’t be in hospital for too long.
"Thanks for the 1000s of you showing concern. England’s greatest ever goalscorer is still with us and here’s hoping he’s home soon."