The academy would include a full-size, international standard artificial grass pitch, six five-a-side courts and a clubhouse, including a gym, to Mather Avenue in Allerton.
Dalglish told liverpoolfc.tv: "The reaction to the Gosforth centre from the community has been fantastic. They really appreciate the level of facilities it offers.
"It is really important for us to work with residents and it was interesting to hear what they had to say.
"This centre would be built to Sport England specifications because people do not want to get changed by the side of a pitch these days.
"I also believe if you provide decent facilities for children, you will get a bit of respect back from them."