The report claims the French international was just too powerful for Liverpool's gym, and knackered the weight-lifting machine within minutes of starting his medical.
Sakho eventually completed his £18m switch from Paris St Germain on transfer deadline day, and this week revealed the story is true.
"That's true," Sakho told the Daily Star. "Strength is one of my attributes and one of the machines did break.
"Something went wrong with it so they had to fix it - not reinforce it.
"I am a defender and I need to use my strength - but I still need to fill out more and bulk-up to progress."
The France international made his Liverpool debut in the 2-2 draw at the Liberty Stadium against Michael Laudrup's Swansea on Monday night.
He's in line to face Southampton tomorrow, as the Reds look to maintain their good run of form that's seen Brendan Rodgers's club climb to the top the Premier League table.
And Sakho insists he came to Anfield to play with the best and compete for Premier League titles.
"I have been brought here to fill a need of the club," Sakho continued. "The most important thing is to come here and wear the shirt with pride and to take the club as high as possible.
"This is a new page in the history of Liverpool and I want to make my mark on that page.
"I came here for the football, not the money. I had a year left on my contract and in four months I could have gone on a Bosman. I put football and the chance to move here above any personal gain."
The 23-year-old is a former-Paris St Germain captain, and along with Sporting Lisbon youngster Tiago Ilori, was the club's final piece of business in the summer window.