Dalglish, who won over 30 trophies for Liverpool as a player and a manager, announced the diagnosis on social media.
"As my inadvertent social media post has indicated, I am currently undergoing treatment for cancer. Unlike my mobile phone use, the treatment is going well," the 75-year-old wrote on Instagram.
"Ideally, this would have remained private because that's the way it should be, but my useless technology skills have forced my hand.
"Obviously, I did not mean to make this matter public, so I would appreciate it if the privacy of my family and myself are respected."
Dalglish scored 172 goals for Liverpool in 13 seasons as a player, winning six league titles and three European Cups during the Merseyside club's glory years.
He later took charge as manager, guiding the Anfield side to three league titles and two FA Cups in the 1980s.
Kevin Keegan, another prolific former Liverpool forward, revealed on Monday that he has stage four cancer.