The European Clubs' Association (ECA), whose members include around 200 clubs from across the region, said that 92 percent of those questioned in a survey said they wanted the two competitions to continue to exist in parallel.
Seventy-five percent were "satisfied" or "extremely satisfied" with the format of European club competitions according to the survey, conducted among 87 clubs from 36 countries.
The only significant change they wanted was for the Europa League winners to qualify directly for the following season's Champions League group stage, with 61 percent in favour of the proposal.
"The results clearly show that European clubs are very happy with the current competitions and do not wish to see major changes to their format," ECA, which is meeting in Doha this week, said in a statement.
The Europe League, which has replaced the UEFA Cup, has produced mixed reactions, with many clubs fielding reserve teams in matches and critics saying it is too big and complicated.
The Champions League group stage is often criticised as being too predictable with the same teams qualifying for the last 16 year after year.
ECA said that clubs could not agree on the proposal from European soccer's governing body UEFA to abolish third-party ownership of players.
"ECA will further assess the merits and the impact of third party ownership on the game and the repercussions of a possible ban," the statement said.
Third-party ownership is when the transfer rights of players are wholly or partially owned by the footballer himself or a company, instead of just the player's club.
The practice is banned in England, France and Poland but allowed in many other countries. It is especially prevalent in Brazil.