No, it is something he came up with himself. He received advises from NASA and the PR people, but in the end it was his decision to say what he said, and as far as we know he came up with it himself. In one regard he did receive a suggestion which was more or less an order: he was to avoid the topic of religion.

On Apollo-8 (first mission which orbited the moon) the mission commander, Frank Borman read the book of Genesis on live TV, and there was some fallout from it NASA didn't want to deal with again. That's why Armstrong was asked to avoid the topic of religion. Also for this reason it was unannounced and not shown on TV that Buzz Aldrin had wine and wafer with him, and had a private communion after the landing of the Lunar Module.

There is also a funny anecdote which is told every time this topic is mentioned.

The commander of Apollo-12, Pete Conrad, was friends with an Italian journalist, Oriana Fallaci, who was convinced that the famous words were given into Armstrong's mouth by NASA. Pete Conrad of course denied this vehemently, and told Ms Fallaci, that he can say whatever he damn pleases on the occasion of his own landing. The lady was unconvinced, so Conrad offered to bet 500 USD that he will say: "Whoopee! Man, that may have been a small one for Neil, but that's a long one for me." Namely Pete Conrad was a short man by astronaut standards, actually he was the shortest in the whole corps, while Neil Armstrong was a rather tall man.

Needless to say, Pete Conrad did utter the agreed sentence on live TV, though whether or not he collected his win, I do not know.

Source: Andrew Chaikin: A man on the Moon

To add to what u/Uggosxa_non__coronat has written - it's generally agreed-upon that Armstrong came up with the line himself.

There's some controversy over when Armstrong thought of the line. After the mission, Armstrong told inquisitive reporters that he'd thought up the phrase on the spot. However, some years after the fact, Neil's younger brother Dean Armstrong claimed Neil had thought of the line several months in advance.

During a a family board game night playing Risk, Neil showed his brother what he wanted to say:

"He slipped me a piece of paper and said, 'Read that.' I did.

"On that piece of paper there was, 'That's one small step for man, one giant leap for mankind.' He says, 'What do you think about that?' I said, 'Fabulous.' He said, 'I thought you might like that, but I wanted you to read it.'"

Later on in the interview, Dean corrected hinself, saying the paper had said "that's one small step for a man."

Dean's account is a little controversial. It contradicts what his brother said after the mission - although Neil may very well have been trying to brush off reporters, which would be in keeping with his tendency to avoid talking about himself. I'm personally inclined to give it credence, since Neil was known for his meticulous preparation and it seems unlikely he'd leave such important remarks totally unplanned.