Mam, 21, continues to receive support from the Broncos after the toughest of weeks following the incident in Las Vegas.
Leniu has since admitted to calling Brisbane's No.6 a "monkey" during the Roosters' 20-10 win in the NRL's season-opening double header.
Broncos assistant coach John Cartwright said Mam would play against South Sydney next Thursday in round two, adding the five-eighth was in the best possible environment.
"As a footballer, the best place to be is with your teammates," Cartwright said.
"I love the way they all pulled together and the fact we're all here together today (is great).
"He's had plenty of support … (he's) a great young kid, Ez, and very popular within the group. He will be fine.
"He is very level-headed. He's dealt with it the way it had to be dealt with.
"The club's dealt with it and it's up to the NRL now."
The NRL judiciary will consider Leniu's punishment next week.
Skipper Adam Reynolds, who sustained a right knee injury in the loss to the Roosters in Las Vegas, went through his paces initially with the rehab group as the Broncos trained at Pizzey Park on the Gold Coast on Friday.
"Reyno is a little bit sore," Cartwright said.
"He got a bit of a bump on the knee. I don't think it's anything major.
"He was out there doing 80 per cent of stuff today. It's Friday and he's still got six days to get right for the game."
Cartwright was optimistic No.7 Reynolds would take his place in the side to play the Rabbitohs.
Lock Patrick Carrigan was also doing rehab but is not in doubt for round two.
"It's just general soreness," Cartwright said.
"It was a pretty light session today. It was just about getting them moving.
"The guys that were sore from the game and travel backed off the speed a bit."
In other promising news for the Broncos, second-rower Brendan Piakura trained with a no-contact bib after suffering a concussion against the Roosters.
"He's just got to follow the protocols for the concussion," Cartwright said.
"Every club now is fully aware of what has to be done. He will be available time-wise, but it will come down to how he passes his tests."
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