Greaves, who scored a record-breaking 266 goals for Spurs across all competitions between 1961 and 1970, spent a comfortable night in hospital and is waiting on further test results.
He came through the ranks at Chelsea, netting 132 goals in 169 matches before joining Italian giants AC Milan.
The striker returned to England when joining Spurs for £99,999 in December 1961, winning two FA Cups and the European Cup Winners' Cup at White Hart Lane, before joining West Ham.
He was also a member of England's 1966 World Cup-winning squad, and scored 44 goals in 57 appearances for his country.
“Jimmy is such a great guy,” said Redknapp, who played with Greaves at West Ham in the early 1970s.
“You talk about good players, Jimmy was a genius.
“As a 17-year-old he scored five goals in one game against a Wolves side that had the England defence!
“He’s a few years older than me and I used to watch him, we rarely got any football on TV, but we might have had England schoolboys on and you’d see Jimmy play and he was just an incredible player even at that age.
“I would think nobody taught Jimmy, he was just a one-off."
Speaking to Talksport, Redknapp added: "I couldn’t speak highly enough of him, he just had this amazing ability to score goals, he never broke the net, he just used to roll the ball in the corner, send the goalie the wrong way or walk around the goalkeeper and score.
“It was great to have Jim come to West Ham even if it was at the end of his career.
“Just to be around him was special, he was that good.”
An update on Facebook from JimmyGreaves.net said "no news is good news at the moment" and that Greaves had spoken to his wife Irene on the phone.
The post added: "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."