Krasnodar midfielder Mamaev and Zenit Saint Petersburg forward Kokorin are facing a five-year jail term after video footage caught them attacking two Russian trade ministry officials in an upscale Moscow café, AFP reported.
The footage showed one of the officials, Denis Pak, an ethnic Korean, being hit with a chair while eating a meal.
Now the former Russian international players, who have courted controversy in the past, could be banned for life from playing in Russia.
"This case is unusual in terms of our football and the league has addressed a request to the ethics committee of the Russian Football Union to impose a lifetime ban on Mamaev and Kokorin," Premier League spokesman Sergei Alekseyev said Wednesday.
Although they have not yet been formally charged, the pair also face up to five years in prison over the incident.
"I think law enforcement agencies will qualify this as hooliganism and punishment for this is quite severe – up to five years in prison," Igor Lebedev, a member of the RFU's executive committee, said in televised remarks.
Krasnodar has pledged to terminate Mamaev's contract while Zenit has condemned Kokorin's role as "disgusting". The Saint Petersburg club removed all t-shirts bearing his name following reports of the attack.
Pak's lawyer Gennadiy Udunyan earlier told Russian state television, "They started to mock (Pak's) ethnicity". The players then allegedly assaulted Pak when he made a critical comment.
He added, "He has a concussion."
Before the cafe assault the footballers attacked the driver of a television host and damaged her Mercedes in a separate incident on Monday.
The driver was hospitalized with injuries and a criminal probe was opened.
On Tuesday, Russian President Vladimir Putin's spokesman Dmitry Peskov said the Kremlin – "just like the whole country" – was aware of the incident and described the video as "rather unpleasant".
'Lowlifes who went berserk'
Commentators, meanwhile, were keen to underline the players were not part of the Russia team that punched above its weight to reach the quarterfinals as the host of the World Cup this summer.
"We should specify that those two...are not currently members of the national squad," Igor Rabiner, a columnist for the Russian daily newspaper Sport Express, told AFP.
Kokorin last played for the national side in late 2017, while Mamaev was last selected in 2016.
Rabiner added, "The players who represented Russia at the World Cup dramatically changed the country's attitude to the game with their successful performance and that is diametrically opposed to this pair's deeds."
It is not the first time the players' behavior has raised eyebrows.
The RFU suspended the pair in July 2016 after a video emerged from a Monte Carlo nightclub in which Mamaev and Kokorin allegedly spent $296,000 on a champagne-fueled party following Euro 2016, where Russia flopped.
Kokorin, who sat out this year's World Cup with a knee injury, later apologized for his behavior and was welcomed back into the national team.
Mamaev last played for Russia at Euro 2016.
"Now they're just lowlifes who went berserk," Rabiner added. "Just ill-bred people who went crazy on the huge money that they receive from their clubs."