Beaumont will meet the 12 English clubs next Wednesday and is prepared to use his influence by acting as a mediator in a Premiership TV deal 'breached contract'
The Premiership and French clubs have served notice on the current European participation agreement, seeking changes to the qualification system and greater financial rewards from 2016.
Premiership Rugby agreed a £152 million contract with BT Vision, with the aim of establishing a "dazzling new European tournament" when the current accord ends.
But the PRO12 clubs have so far rejected Premiership Rugby's proposals, and if there is no agreement within the next six months that could be the end of the Heineken Cup.
Beaumont brokered a peace deal when the RFU were involved in a television rights war in 1999 and is ready to step into the breach for the English clubs.
"As chairman of the RFU and being involved in the Six Nations we have a meeting coming up in Rome and this (the current European row) will be an agenda item," Beaumont said.
"I would like to think with the contacts that I have got and the relationships I have built up amongst our neighbours I will try and use my best endeavours. That is what the RFU wants. We are keen to resolve this situation. We don't want to be at loggerheads with our neighbours all the time or the clubs, why would we?"
Beaumont is looking to help Premiership Rugby despite being told that the English clubs may have breached their contract with the RFU in signing the BT deal because it was not sanctioned by Twickenham.
- Premiership Rugby