The hearing, on Tuesday, heard from several experts about the problem which was recently highlighted by the case of Barcelona superstar Lionel Messi.
The Argentinian was given a 21-month suspended jail sentence after being guilty of tax fraud amounting to some €4.1m.
Another high-profile case is that of Real Madrid player Cristiano Ronaldo, who reportedly channelled €63.5m to an offshore account in the British Virgin Islands, saving €35m in taxes in the process.
Dutch journalist Merijn Rengers, who has probed the problem of tax evasion in football for the European Investigative Collaboration, also claimed that Manchester United manager José Mourinho had avoided tax after he moved €12m to a Swiss bank account.
The investigative reporter told the latest hearing of the Panama inquiry committee the problem of tax evasion and avoidance had become an epidemic in football.
He said, “There seems to be a lack of authority and some of the biggest clubs and players systematically channel money outside of European tax jurisdictions.”
Rengers said, “During our investigations we were told by agents and others in the game that, ‘this is how it has always been, so leave us alone’.”
Gregor Reiter, of the European Football Agents Association, based in The Hague, hit back by making a robust defence of football agents.
“Contrary to the picture often portrayed, not all football agents are crooks and 95 per cent of transfers are done correctly and according to the rules and regulations,” he said.
“Agents are an important part of football and we hope to keep it that way.”
He told MEPs that before 2015, some 70 per cent of transfers were done with a non-licensed agent, but that the situation had improved since then.
Under new rules, agents, for example, were no longer paid a transfer fee, he said.
But another keynote speaker, Uefa lawyer Julien Zylberstein, admitted his organisation was limited in combatting tax evasion in the sport.
He told the meeting, “Tax evasion is a clear threat to the social value of the sport, but this is really for the national tax authorities to intensify efforts to tackle the problem.
“The powers of Uefa in this sphere are limited.”
Even so, he pointed to what he said was the success of the financial fair play regulations, introduced seven years ago, which had helped reduce European football club losses from some €1.7bn in 2010 to €300m in 2015.
A representative of Fifa, the world governing body of football, told the committee the organisation took the issue “very seriously.”
S&D group member Jeppe Kofod cited an online campaign mounted by Barcelona which appeared to defend Messi.
He said the slogan, “We are all Lionel Messi”, was “very questionable, given the conviction.”