The RFU said it would conduct an internal investigation and also asked for an explanation from state-controlled Channel One television after a programme last week accused some players of drinking and smoking hookah pipes before the November 14 first leg.
Favourites Russia won the first leg 2-1 in Moscow but were eliminated by Slovenia on away goals following a 2-2 aggregate draw after losing the return match in Maribor 1-0.
The RFU also asked for explanations from the Marriott Grand hotel, the national team's headquarters, after hotel employees appeared on the programme accusing players of partying on the night before the Moscow match.
"On Monday, the RFU sent an official letter to the heads of Channel One and the Marriott Grand, asking them to provide explanations about the reliability of the reported information," the FA said on its website.
The RFU said it would wait for an official response from the relevant parties before making any decisions and would conduct its own investigation after talking to the coaching staff.
Parliament members have demanded a thorough investigation into the allegations which have created huge negative publicity for Guus Hiddink's team, who are still reeling from their failure to qualify for next year's World Cup in South Africa.
All the players have strongly denied the accusations while the Berezutsky brothers, Vasily and Alexei, have said they would go to court to clear their names.
Hiddink said he trusted his players.
"I've heard something (about the allegations)," the Dutchman was quoted as saying in Monday's Sport-Express newspaper.
"Channel One is respected in Russia, it wouldn't repeat unfounded allegations and rumours. You must have proof. I repeat you must have direct proof.
"Statements saying the players were sitting in a restaurant until five in the morning on the day of the game are quite serious. If I had proof of that, every player involved in it would have been immediately dropped from the national team.
"We've had some small incidents during my time as Russia coach and I warned the players about the consequences. Since then everything has been fine and I have no proof to doubt it."
