He said Bush's "quality of life had deteriorated a lot" in recent months, but that near the end he was able to talk by phone with his adult children, including former President George W. Bush.
Sully is to make his final journey with his old companion to Washington, DC, on Monday, a report says.
In Washington, Bush will lie in state in the rotunda of the U.S. Capitol from Monday at 7:30 p.m. EST until Wednesday at 8:45 a.m. EST. Barbara Bush died on April 17 at their Houston home. Despite the fact that Trump's rise to power included lambasting past presidents, including both Bushes, the President has responded to Bush's death with repeated laudatory comments.
George H.W. Bush is set to embark on his final tour of Washington, the US capital that is remembering the 41st president's lifetime of public service that began in the navy during the Second World War, ended with one term as the country's leader, and was characterized by what admirers say was his innate decency, generosity and kindness.
Bush's son Jeb, the former Florida governor, retweeted the photo with the simple words "Sully has the watch".
A moving photo of the late President George H. Rest In Peace, 41.
Social media users thanked Sully for his services and commented on his and dogs' loyalty generally towards their owners.
Bush received the two-year-old Labrador in June from America's VetDogs charity.
Sully the dog will be travelling with the casket on the flight from Texas to Washington DC on Monday. His remains are scheduled to arrive at Andrews Air Force Base in Maryland in the afternoon.
On Sunday, Bush spokesman Jim McGrath posted a picture of Sully lying by Bush's flag-draped casket, which quickly went viral. "As much as our family is going to miss this dog, we're comforted to know he'll bring the same joy to his new home, Walter Reed, that be brought to 41", the 43rg president wrote.
One of Bush's last wishes was for Sully to continue to serve and he will return to NY for the holidays before heading to Washington, D.C. There, he will join the Walter Reed National Military Medical Center's Facility Dog Program.
The service dog is named after Chesley "Sully" Sullenberger, the US Airways pilot who safely landed a passenger plane on the Hudson River outside New York City in 2009.