Apart from stating that Wisdom, 22, has signed a "long-term" deal, Liverpool did not reveal the durations of the contracts, but former Côte d'Ivoire centre-back Toure, 34, is believed to have agreed to a one-year extension.
"Liverpool FC are pleased to announce Kolo Toure has signed an extension to his contract with the club," Liverpool said in a statement on their website. "The centre-back will remain with the Reds after putting pen to paper on the new deal."
Meanwhile, the Football Association have announced that Liverpool's 19-year-old winger Jordon Ibe has withdrawn from the England U-20s squad for the Toulon Tournament due to a recurring knee injury.
Ibe has been one of the few positives of a disappointing season for Liverpool and was last week rewarded with a new five-year contract.