United's total revenue has increased from £323.7m to £346.5m in the last season, but they've still been overtaken by Bayern Munich in Deloitte's Football Money League report.
That has been put down to the German club's UEFA Champions League and domestic success, helping increase their revenues by 17 per cent to £352.5m.
The report puts five English clubs in the top 20. Sheikh Mansour's Manchester City have risen to sixth position in the table, putting them above Premier League rivals Chelsea (7th) and Arsenal (8th) for the first time.
Tottenham Hotspur maintained their 14th position. Deloitte say other English clubs such as Everton, Newcastle United, and West Ham United could challenge for top 20 positions next season because of the new Premier League broadcast deal.
The combined revenue of the top 20 clubs, almost all of which grew during 2012/13, increased by 8 per cent to £4.4bn, much faster than the global economy.
Real Madrid top the money league for the ninth consecutive year, beating Manchester United's previous eight-year run, with total revenue of £424.2m. Barcelona hold onto second spot.
Austin Houlihan, senior manager in the Sports Business Group at Deloitte said: "Whilst Manchester United drop one place in the money league, a number of the club's recent commercial deals will boost revenue in 2013/14, so this fall to fourth place may only be temporary.
"These deals, combined with the impact of the improved three-year Premier League broadcast deals from 2013/14, mean they are likely to get close to the €500m (£408.7m) revenue mark in next year's money league.
"Beyond 2013/14, consistent qualification for the Champions League is key in United challenging to regain top spot in the money league, a position it last held in 2003/04."
Dan Jones, partner in the Sports Business Group at Deloitte, said: "Real Madrid remain firmly at the top of the money league, even though the club experienced a trophy-less end to the 2012/13 season.
"Despite tough economic conditions, particularly within Spain, the club's ability to generate substantial commercial revenue both domestically and internationally is central to their success. This helped widen the gap to their nearest rivals in the money league, FC Barcelona, to €36m (£29.4m)."
In addition, Paris Saint-Germain climb into the top five. The club's revenue has almost quadrupled to £326m since 2010/11, and includes commercial revenue of £208.2m - the highest ever single revenue source from a football club.
Houlihan added: "PSG are the fastest climber in this year's money league, claiming the highest ever position for a French club. They are the country's sole representative in this year's top 20.
"We expect to see them become a mainstay in the top five in years to come, backed by their ambitious Qatari owners and strong commercial support.
"The high-profile signing of David Beckham in the second half of the 2012/13 season only served to enhance the club's worldwide profile.
"Importantly, commercial success off the pitch is translating into improved on-pitch performance for the club, including winning their first Championnat title in 19 years."
Manchester City moved up a place to sixth in the standings and Houlihan insists City have made stride in terms of their global presence.
"Manchester City's growth this year is particularly due to commercial revenues," he said. "Like a lot of other clubs they are growing their brand internationally and that has contributed to significant commercial growth."
Galatasaray and Fenerbahce's appearance in the money league, following successful campaigns in European competition, make it the first time since 2005/06 that two clubs from outside the 'big five' European countries appear in the top 20.