The clubs provide players for the national team, which crashed out of the tournament in the pool stages, resulting in a missed opportunity to boost both the sport's profile in England and attendance figures at Premiership games.
"We should have more of an input as to how they use our assets," Tony Rowe, chairman of Exeter Chiefs, told the Times on Friday.
"We could be asked at least to attend a meeting. Each club has invested a lot of money in those players that go to play for England, but we have no input as to how they are coached."
Bath chairman Bruce Craig called for the clubs to be involved in the appointment of the next England coach.
"We should have a major input into how it should be structured and who the head coach should be," he said.
The clubs also want Rugby Football Union Chief Executive Ian Ritchie to call upon their expertise during his review into England's performance at the World Cup.
"We are talking to them about it and they are accepting that we should have a voice," Craig said.
The RFU is in the process of formalising a way for the clubs to contribute to the review, the newspaper reported, although whether they will get a say in appointments is unclear.
"If they want this to be a successful process, they should talk to the clubs," said Simon Cohen, chief executive of Leicester Tigers, the Premiership's most successful club.
"There is a huge amount of expertise in the Premiership and it'd be nice to think that they would take advantage of that."
Stephen Vaughan, managing director of Gloucester, said the World Cup was important to the clubs.
"We are stakeholders in the England team and we have a multitude of expertise," he said.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Ed Osmond)
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