The England international struggled with injury last season following knee surgery, but during the campaign Ancelotti labelled him "a genius" and said he was 100% sure that the 28-year-old's future was with the London club.
But talks broke down over a new deal, with Cole citing "political rather than footballing reasons", and the former West Ham star was allowed to leave on a free transfer.
However, Ancelotti said the capture of Israeli international Benayoun, 30, will add an extra dimension to Chelsea's midfield.
"He's an intelligent player, tactically he knows everything very well," Ancelotti added. "I tried to put him as a right midfielder in this pre-season and he can also play in his usual position as a winger.
"He has to train, to improve his condition but I think for us he is a good player."
Benayoun spent three years at Anfield after signing from West Ham, scoring 29 goals in 134 games from midfield.
Carlo Ancelotti on the Premier League's new squad rules
While home-grown players must have been registered to the Football Association or Welsh FA for three years prior to their 21st birthday there is no requirement for them to be English and Chelsea have promising youngsters Jeffrey Bruma, Patrick van Aanholt, Gael Kakuta, and Fabio Borini, along with the English Josh McEachran, in their ranks.
"I don't think we have a difficulty to put a squad in. We have the right number of foreign players.
"I am happy because it is important for our academy - they are very good players, they need to stay with us and will have more chances this year.
"I know them very well. We followed them for the last year and it is the time for them to be involved in the squad. I don't know how many games they can play this season but we need to have these young players in our squad."
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