The suspect, believed to be an Egyptian national, was shot in the stomach and seriously wounded after lunging at soldiers with two machetes on Friday.
Investigators decided to question him in hospital after his condition improved, the source said.
The man "is refusing to speak to investigators for now", the source added.
The suspect has been held at a Paris hospital since Friday's attack near the historic museum, which thrust the issue of security back into the headlines three months ahead of the French presidential election.
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Investigators believe Hamahmy rented an expensive apartment near the Champs Elysees.
Police were examining Hamahmy's Twitter account after around a dozen messages were posted in Arabic just minutes before the attack.
"In the name of Allah... For our brothers in Syria and fighters across the world," he wrote, before referring to the Islamic State jihadist group in another tweet a minute later.
Speaking to AFP in Cairo yesterday, a retired police general, Reda El-Hamahmy, said he believed the wounded suspect was his son, Abdallah, who had been in Paris on a business trip.
"He went on a company trip and when it was over visited the museum. He was supposed to leave on Saturday," he told AFP, saying his son was married and his pregnant wife was currently staying in Saudi Arabia with their seven-month-old son.
"He is a simple guy," he said. "I can show you pictures where he has no beard," he said. Beards are often grown by devout Muslims.
Over the past two years, France has suffered a string of bloody attacks by Islamic extremists and has been under a state of emergency since November 2015.