The 31-year-old left Paris Saint-Germain in the summer for the Saudi Pro League club in a £69million deal plus add-ons.
Following a long injury layoff, Neymar made his debut in 6-1 victory over Al-Riyadh on September 15.
The Brazilian was sidelined with an ankle injury, having been on the treatment table for six months.
He has since made two appearances, but was an absentee as Al-Hilal defeated Al Jabalain 1-0 in the King Cup of Champions on Monday.
Spanish publication SPORT claimed Neymar had already fallen out with Jesus.
read more on neymar
I played with Neymar for Brazil but Spurs star was the best - he should have a Ballon d'Or
Neymar decision booed by Al Hilal fans as superstar makes debut
The report added the player had an altercation with the manager in the dressing after a match and has been reprimanded him for his behaviour.
Neymar has since quashed these rumours, taking to Instagram to express his displeasure.
An Instagram account named fiqueiputomesmo_, also backed the fallout claims.
In response, Neymar said: "Lies... Y'all got to stop believing these things, pages like this... with millions of followers you can't keep posting fake news!
Most read in Football
Sancho exile continues, Chelsea legend leaves club, Carabao Cup build-up
Sancho banned from all first-team facilities at Man United as Ten Hag stand-off goes on
Jermaine Jenas apologises for abusive criticism of referee at Arsenal vs Tottenham clash
Arsenal 'optimistic' on Declan Rice injury and hope he'll be available for mammoth clash
"With all due respect in the world, I ask you to stop this. This is a lot of disrespect."
Previous reports have also suggested the former PSG forward is eyeing a return to boyhood club Santos, as he looks to earn a place in the Brazil squad for the 2026 World Cup.
There had been talk that the South American ace had signed a four-year deal in the the Gulf State, but it is in fact two years, according to Brazilian journalist Ademir Quintino.
"During conversations with friends of Neymar Senior and Neymar Junior, I received the information that they did not sign a four-year contract with the Saudis but rather a two-year contract so he can return (to Santos) a year before the World Cup," Quintino said.
"Neymar approached Santos and asked to return. I have friends in common with Neymar, whom I will not name, but he has a very strong desire to return to Santos."
Al-Hilal are currently second in the Saudi Pro League table, and take on Al-Shabab in the league on Friday, and it remains to be seen whether Neymar will be involved.