Gerrard, who is manager of Aston Villa, won the Champions League, the UEFA Cup and two FA Cups during a 17-year career at Liverpool and won 114 England caps, playing at six major international tournaments.
His former Madrid and Uruguay teammate Luis Suarez first made the comparison with Valverde, 24 -- who is in the best form of his Madrid career, scoring in his last three club games -- in an interview with the newspaper Marca on Saturday.
"I agree [with Suarez], yes," Ancelotti said when asked about the comparison in his news conference ahead of Madrid's LaLiga clash with Osasuna.
"[Valverde] has a lot of the same things that Gerrard had. It's good for him to be compared with a player who had that success. Federico has everything to get to Gerrard's level, and even more."
Valverde joined Madrid as a teenager from Penarol in 2016, and initially featured for reserve team Castilla before making his first team debut in 2018.
The Uruguay international midfielder has become an increasingly important player for Madrid over the last three years, providing the assist for Vinicius Junior's goal in last season's 1-0 Champions League final win over Liverpool in Paris.
With four goals this season -- three in LaLiga against Celta Vigo, Real Mallorca and Atletico Madrid and one in the Champions League against RB Leipzig -- it is already his best campaign in front of goal.
Meanwhile, Ancelotti confirmed that Karim Benzema will be back from injury for Sunday's game with Osasuna at the Bernabeu, while Luka Modric is expected to return next week from a hip problem picked up on international duty with Croatia.
"[Modric] had a little problem, it isn't very serious," Ancelotti said. "He'll be close for [Madrid's Champions League game with Shakhtar Donetsk on] Wednesday. He'll train on Monday and we'll see if he's comfortable. If not, he'll play in the league at the end of the week."