Monaco vice-president Vadim Vasilyev says the Ligue 1 club turned down a succession of offers from Manchester United before agreeing to part with Anthony Martial for a fee of £57.6 million.
Martial, 19, signed for United earlier this week in a deal reported to be worth £36m up front.
French media reported that the transfer fee could eventually rise to €80m (£58m) when bonuses were included, which would make him the most expensive French player in history.
And Vasilyev appeared to confirm that information as he said the final price would be £57.6m when "very realistic" bonuses are taken into account.
"Since last week United started to make offers which we declined several times -- £21.6m, £28.8m, £36m, even £50.4m with bonuses.
"On Sunday the player got such an offer that he couldn't have declined. He asked us to find a solution and on Monday morning Manchester United made an offer to Monaco which the club couldn't refuse.
"It's absolutely unique. It's the price of Luis Suarez or Neymar -- the best players in the world.
"Right now English football is on a different financial level and if Manchester United decides to buy somebody, it's very hard to stop them."
On Thursday French newspaper Le Parisien indicated the transfer included three bonus payments, each worth €10 million.
The first will be paid when Martial scores 25 goals in all competitions for United and the second will be triggered if he earns 25 caps for France between now and June 2019.
The third will come into effect should Martial win the Ballon d'Or as the world's best player between now and the end of his four-year contract at Old Trafford.
The paper also claims that Martial will receive a bonus of €1.15m every time that Manchester United qualify for the Champions League.
Meanwhile, Martial's France teammate Eliaquim Mangala has warned that the former Lyon player could initially find life in the English Premier League tough.
Last season Mangala, 24, endured a difficult start after making a €54m move to Manchester City.
"He's going to be looked at very differently because Manchester United spent a lot of money him," the former Porto defender said.
"You'll have to see how he'll be managed by his family and his club because that will be important.
"He has to concentrate on his football. The rest is part of the world of football, which is normal. You see some very big transfer fees these days and when you compare them to some prices in the past you say 'sometimes it's going a bit too far.'
"I don't think anybody is worth 50m or 80m or 100m but that's part of business and of football.
"It's up to him now to make progress on the pitch. His first season could be difficult because the Premier League is totally different. It's a difficult league but I hope he'll be well guided."