The chief executive of HM Revenue and Customs, Jon Thompson, has told MPs he would like to see a review of the way footballers can reduce their tax bills.
He said payments to them for their image rights were “the most significant risk in football” faced by HMRC.
Some footballers and entertainers have income from the use of their names and images paid into offshore accounts without tax being deducted.
Mr Thompson told MPs, “I think if it was me, I would want to review this.”
He added: “It is quite difficult to explain to a football fan that that is the law.”
The HMRC’s head of enforcement, Jennie Grainger, said that 43 players, eight agents and 12 football clubs were under investigation.
She added that an extra £150m of revenue had been raised from football over the past two years.
The officials also told MPs on the Public Accounts Committee that HMRC had seven criminal investigations under way and had made arrests following publication of the Panama Papers, which provided a huge amount of information about the tax affairs of wealthy individuals.
The action follows the formation of an inter-agency task force six months ago, including HMRC, the FCA, the Serious Fraud Office and National Crime Agency.
At the weekend, House of Commons public accounts committee chairwoman Meg Hillier said the tax affairs of football manager Jose Mourinho should be investigated by British officials, following allegations that he used offshore companies to reduce his tax bill.
Mourinho is accused of moving millions of pounds of earnings to the British Virgin Islands to avoid paying tax.
According to reports in the Sunday Times, Portuguese-born Mourinho, 53, placed £10m (€12m) into a Swiss account owned by a British Virgin Islands (BVI) firm, which it suggests has no employees.
The newspaper also claims that Real Madrid star Cristiano Ronaldo used bank accounts and companies in Ireland, Switzerland and New Zealand to process substantial earnings for their image rights.
However, Mr Jorge Mendes – the agent for both Mourinho and ex-Manchester United player Ronaldo – denies both claims.
He says both men were fully compliant with UK and Spanish tax rules.
The statement added that the allegations stemmed from a cyber-attack earlier this year on some sports agents, details of which were prohibited by a Spanish court from being published.
HMRC said it would not comment on named individuals, but took “all allegations of tax evasion extremely seriously” and “always investigates allegations of fraud together with any intelligence provided”.
The head of HMRC will appear before Ms Hillier’s committee – which is responsible for overseeing government expenditure – on Friday.
Manchester United said the allegations related to events before Mourinho’s arrival at the club and so it would not comment.