Speaking last week, Prince Edward said Philip was "a lot better", but admitted he was frustrated to be in hospital.
The Duke has only so far had a visit from Prince Charles who saw him on February 20, but one royal correspondent said the lack of other visitors was unsurprising.
Philip's grandson, Prince William, previously said his grandfather was doing "ok" and that hospital staff were keeping an eye on him.
According to Dickie Arbiter, who spoke on "The Royal Beat", the dad-of-four wanted to talk to the Duke of Cornwall to "lay the ground". My guess is that he will come out, he will walk out and he will go back to Windsor.
In Tuesday's last update (23), the Palace said, "He is comfortable and responds to treatment, but should not leave the hospital for several days".
Coronavirus Northern Ireland: Three further deaths and 276 new cases reported
It's the fourth day in a row that more than 40 new confirmed cases of Covid-19 have been reported in Limerick. Malaysia has recorded 2,461 new COVID-19 cases today which brings the total number of infections to 280,272.
The Queen's husband, 99, was taken ill in London last week and has now been transferred from King Edward VII's Hospital to St Bartholomew's Hospital to continue his treatment.
Philip spent 14 days and 13 nights there - his longest stay in a hospital to date - before he was transferred on Monday to St. Bartholomew's Hospital, also in London, where doctors will continue to treat him for an infection, as well as undertake testing and observation for a preexisting heart condition.
"So we keep our fingers crossed".
The 99-year-old husband of Queen Elizabeth II was moved from King Edward VII's Hospital, where he has been treated since February 17, to St. Bartholomew's Hospital, which specializes in cardiac care. "I think it affects all of us, and then you can only look at the clock so many times and the walls are very interesting".
The Earl of Wessex added: "We received some bright and charming messages from all kinds of people and we really appreciate it and so does he". During England's current coronavirus lockdown, he and the queen had been staying at Windsor Castle, west of London.
He and the queen, 94, both had the first dose of a Covid vaccination on January 9 due to their age, which puts them in one of the most vulnerable categories.