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The former forward and manager wanted to keep the news private but confirmed the diagnosis after accidentally sharing the news initially in an "inadvertent social media post".
"I am currently undergoing treatment for cancer," Dalglish, 75, wrote on social media. "Unlike my mobile phone use, the treatment is going well.
"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.
"As ever, thank you to the wonderful medical staff who have shown incredible care and discretion, not just for me but for many, many others. They are a credit to themselves."
Dalglish scored 167 goals in 320 appearances for Celtic between 1969 and 1977 before going on to make 515 appearances for Liverpool.
The legendary forward scored 30 goals in 102 caps for Scotland.
In a statement, Liverpool said: "The support, best wishes and love of everyone at Liverpool FC are, and will be, with Sir Kenny and his family.
"The club would also like to underscore his request for privacy moving forward."

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