The former Scotland defender had received well wishes from across the game
when Liverpool confirmed on 9 June that he was "seriously ill.
But on Sunday a family statement on the club website said that Hansen, 69, will "continue his recovery at home".
“Alan, Janet, Adam, Lucy and family would like to thank everybody for their wonderful messages of love and support”
“It has been overwhelming and has helped enormously.
“We also hugely appreciate the ongoing respect that has been shown for our privacy as Alan continues his recovery.”
Hansen spent 14 years with Liverpool, winning eight First Division titles
three European Cups and two FA Cups during the 1970s and 1980s.