Wasps made 167 players and staff redundant, British media reported, after going into administration on Monday, a week after they were suspended by the RFU.
The RFU said in a statement that it was speaking daily with administrators and the league to examine whether there was any possibility of a takeover.
"The news Wasps are now in administration is desperately sad. We believe it is right to keep working with all parties to give the club the best chance of long-term survival if at all possible," RFU chair Tom Ilube said.
"We all feel for the fans, players, volunteers and everyone with a connection to the club."
Former Premiership and European champions Wasps had filed a notice in the High Court last month stating their intention to appoint an administrator to secure their future.
RFU regulations state that a club placed in administration during the season will be relegated for the following campaign.
Premiership Rugby and the RFU last week called for more financial transparency and announced plans to review the league's structure in the wake of financial crises at Wasps and Worcester Warriors, who went into administration last month.
"The RFU and Premiership Rugby have been working for some time to develop a sustainable model for rugby to deliver long term prosperity for the sport," RFU chief executive Bill Sweeney said.
"Wasps and Worcester entering administration has accelerated these plans and reinforced their importance."
The RFU and Premiership will face a parliamentary inquiry in November over the two clubs' financial struggles and the sustainability of the sport, the Department for Digital, Culture, Media & Sport said in a statement.
"The RFU and Premiership Rugby have acknowledged the need to set a more sustainable path for club rugby," DCMS committee chair Julian Knight said.
"We will be pressing them to ensure they are putting the foundations in place to guarantee the health of the sport from the top level right down to the grassroots."
