Roma president James Pallotta says Liverpool owner John W Henry felt they overpaid Mohamed Salah last summer.
The Egyptian has enjoyed a season to remember with 31 goals in 33 Premier League games.
Roma chief Pallotta revealed Henry was concerned about the price Liverpool were paying for Salah last summer.
He told ESPN: "He was sort of b****ing a little about, 'Did we overpay? I think we overpaid'.
"And I said, 'I'll buy you lunch'."
Roma were under financial pressure to let one of their big names leave and Pallotta says that allowed Liverpool to pick up “an unbelievable bargain".
He said: "When you look at it now, you can say it's an unbelievable bargain.
"The issue at the time was that when [Roma director of football] Monchi came in, Salah wanted to leave. He had a year left on his contract so in another year you'd get nothing.
"He wanted to go back [to England after a spell with Chelsea] and prove himself, which he certainly has done.
"We can't tell you that anybody else was calling for Salah at anywhere near that kind of price, so there's a lot of teams that have missed out on the great play he's had this year."