Bush, 92, posted a photograph with his son former US president George W Bush on Twitter with the caption: "Big morale boost from a high-level delegation. No father has ever been more blessed, or prouder."
The former US president was admitted to Houston Methodist Hospital last Friday for treatment of a persistent cough.
A spokesperson for the Bush family said on Wednesday that Mr Bush "continues to gain strength" and is looking forward to being released next week.
As is the case with most people his age, Bush has had his share of health issues in recent years.
Mr Bush, who served as US president from 1989 to 1993, received a visit from yet another former president earlier this month - Bill Clinton, who presented him with new socks.