The 26-year-old, who joined the Serie A outfit in 2010 from Clermont Foot, has been linked to a whole host of clubs previously, including Inter Milan, Manchester United and PSG.
It is reported the Morocco international will cost around 6.5m euros (£5.52m), while at least one player from Roma will transfer in the opposite direction as part of the deal.
Benatia told Gazzetta dello Sport: "I haven't signed yet. I'm just waiting for Roma to sort out the details with Udinese. But I have given my word to Roma.
"Others clubs? I don't want to mention any names, but I turned down the chance to play in the Champions League.
"I also rejected offers from two Italian clubs who were chasing me."
Benatia says he will bring versatility to the Roma defence.
"I've always played as a right-sided centre-back in a back-four, but I was also taught how to play in the back-three in Udine. I know how to adapt," he said.
"Am I a hard defender? I've never been sent off in my career, even if I have been close a thousand times because a defender can't just watch an opponent dribble past you.
"A defender has to attack, he has to frighten."
Meanwhile, Roma are also leading the chase for Cagliari midfielder Radja Nainggolan.
Serie A rivals Inter Milan and Napoli are thought to be keen on the Belgian midfielder, who has also been linked with Tottenham and Southampton.