Tottenham say their record goalscorer Jimmy Greaves remains in hospital but "has not tested positive for Covid-19 nor suffered another stroke".
The World Cup winner, 80, was admitted on Tuesday for an unspecified illness.
Greaves, who scored 44 goals in 57 games for England, suffered a severe stroke in 2015.
"Jimmy’s family has asked us to pass on their thanks for all the well wishes and positive messages," added a statement on Tottenham's website.
In a separate statement on Friday, Greaves' friend and agent Terry Baker said: "We have had thousands 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."
Greaves, who scored 266 league and cup goals for Spurs, began his career at Chelsea and also had spells at West Ham and AC Milan.
He hold the record for most top flight goals in English football, with a total of 357.
He is fourth on the list of all-time England goalscorers, behind Wayne Rooney (53), Sir Bobby Charlton (49) and Gary Lineker (48).
Greaves was part of England's 1966 World Cup-winning squad but originally missed out on a medal because he was injured during the tournament's group stage.
After recovering, Greaves was left out of the starting XI for the final and his replacement, Sir Geoff Hurst, scored a hat-trick as England beat West Germany 4-2 after extra time.
The World Cup squad players and the families of manager Sir Alf Ramsey and other backroom staff were finally presented with medals in 2009.