One of those offers came from Martine Hanote who was ready to welcome Mr Hyde into her apartment.
"In Geneva we hide too often this type of problem," she told the newspaper.
But Mr Hyde has chosen to stay among New Zealanders who offered him board.
"Assailed by national and international press, David preferred to contact New Zealand nationals, who like him were involved in international organisations," Tribune de Geneve reported.
"The most important thing he has finally found a roof to sleep under for the next few days."
Mr Hyde previously told the newspaper he searched for a room when he arrived but could not afford the rent in the city, which is one of the world's most expensive places to live.
"I was perhaps naive in coming here but this policy [unpaid internships] makes me furious," he's quoted as saying.
Other interns who took on the six-month positions at the United Nations could only do so with the help of their parents, he reportedly said.
A retired teacher, Ms Hanote opened the doors to her apartment.
"I found myself in a similar situation when I was a student. But at the time I found a student job which was quite simple and the rentals were not as good as today," she said.
One Genevan, who offered Mr Hyde a place at their home, said: "I have a bedroom for him and even a bike."
Another said: "He could use the bathroom and the kitchen if necessary. He must just like animals because we have a dog and two cats."
Some political personalities were also moved by the plight of the young international relations graduate, the newspaper said.
Former national councillor and liberal MP, Jean-Michel Gros was quoted as saying: "There are surely dozens of others, but I am sensitive to his situation. Above all I am not a humanitarian without a soul."
Mr Hyde was amazed by the response to his story, the newspaper said after catching up with him again.
"All these messages of support, it's unbelievable. It was never my intention to solicit the pity and get myself a place to stay," he said.
"I hoped simply that my story could contribute to changing the situation of interns."
Earlier, Mr Hyde told the newspaper he had a difficult weekend when he got caught in stormy weather.
"I did not choose the most waterproof tent in the shop," he's quoted as saying.
Rainstorms had saturated the small plot of land facing the lake where he had been setting up his tent each night.
Describing his living conditions, Mr Hyde said he would don his suit each morning, gather up his gas stove and few possessions, and store them in his backpack which he hid under his desk at work.
A graduate in human relations, he had started his internship at the UN two weeks ago, the Tribune de Geneve said.
After studying for a semester in Paris, he joined a group of interns who go through the international office at Geneva, the newspaper said.
The interns do not get paid, and do not get expenses for transport, board or medical benefits, it said.
"A line to add to the CV serves as payment."
"Only those whose parents can pay have a chance," Mr Hyde told the newspaper.
His family were unaware of his living situation, he revealed.
"They encouraged me and when I received the positive response, everyone was very proud of me at home. The United Nations, Geneva, it is still prestigious."
Mr Hyde had tried looking for a place to live, researching bedrooms and studio apartments, but said they were all "too expensive for me".
"I may be being naive in coming here, but this politics makes me furious. Now, if I leave before finishing I will not have a certificate," he was quoted as saying.
His internship was due to last six months.
But he does not yet know what he will do when it's finished, as a clause prevents him from getting a job at the UN in the six months that follow the end of his work experience.
It's a practice that is often criticised, the newspaper said, blocking young interns from getting a permanent position while maintaining a constant rotation of free workers for the international organisation.
At a May rally, the Geneva Interns Association protested against the "inconsistency of the United Nations, who promotes their values, such as non-discrimination, diversity and participation globally, but do not apply this to their staff", the newspaper said.
However, the UN said it was "not like that".
"There are solutions," Ahmad Fawzi, communications chief with the United Nations, told the newspaper.
"If the boy had done some research he would have found a place to stay. There exist solutions for interns and even lists of families who would host them."
Mr Fawzi was forced to respond to "numerous questions on the subject" after Mr Hyde's story hit the local headlines, the newspaper said, with the issue inflaming international workers.
The UN wanted to help Mr Hyde find a place to stay, Mr Fawzi said, reiterating his desire for change, but saying the balance of power rested in the hands of the 193 member states.
