In a report on the summer transfer window, the Swiss-based CIES Football Observatory said Manchester United and Paris St Germain had paid tens of millions of euros above market rates for top purchases Angel di Maria and David Luiz.

"Our new data analysis has revealed that overall, clubs paid on average 16% more than they invested in the five previous years for players with similar characteristics," CIES said.

"This confirms the ongoing inflation trend of the transfer market at the top end of the football pyramid," it said.

CIES examined football's "Big Five" - the English Premier League, Spain's La Liga, the Italian Serie A, Germany's Bundesliga and the French Ligue 1.

"The inflation trend is mainly due to the sums spent by a handful of wealthy clubs" ready to pay more than a player is worth to get the best talent, said the study.

CIES said that the most inflation-driving deal was Manchester United's British record �59.7 million (75.5 million euros) signing last week of Real Madrid midfielder di Maria.

CIES said that sum was 30 million euros over the right price for the Argentina international, in market terms.

United, who are 20-time English champions, are looking to rebuild following a disappointing seventh-place finish last season and have spent around �150 million in the process.

CIES said that Paris St Germain's fee of 62 million euros to bring Brazilian David Luiz from Chelsea was 29 million euros too high.

The sum was a world record for a defender.

Real Madrid, meanwhile, paid 25 million euros over the odds for World Cup Golden Boot James Rodriguez.

The Colombian moved from Monaco for 80 million euros.

At the other end of the scale, Liverpool's purchase of Mario Balotelli for �16 million (20.2 million euros) from AC Milan was 16 million euros underpaid, CIES said.

Italy striker Balotelli was signed to help Liverpool fill the void left by Luis Suarez, who was another cut-price player.

Barcelona paid �75 million (94 million euros), or 12 million euros under the odds, for the controversial Uruguayan.

CIES said the Catalan club got a good deal thanks to "the existence of buy-out clauses and/or non-sporting related issues".

Suspended by FIFA after biting an opponent at the World Cup, Suarez cannot make his Barcelona debut until October 25.

The third most under-sold player was Spain's Diego Costa, who Chelsea bought from Atletico Madrid for �32 million (40.5 million euros). CIES said that was 10 million euros less than he could have commanded, on current market trends.