The 40-year-old former New York Giants defensive end is currently a host of "Fox NFL Sunday."
The ABC morning show will officially name Strahan co-host in early September, Broadcasting & Cable magazine reported.
Ripa has been without a permanent partner since Philbin, 80, retired from the show in November.
Fifty-nine guest-hosts have sat next to her in the meantime -- including Strahan, "Saturday Night Live" comic Seth Myers, comedian-actor Jerry Seinfeld and New York City news anchor Pat Kiernan.
The Los Angeles Times reported Monday if Strahan gets the job, he is expected to keep working on the popular NFL pregame show.
"Fox NFL Sunday" is aired from Los Angeles, while "Live!" airs during the week in New York.
A spokeswoman from "Live!" told Broadcasting and the New York Daily News she would not comment on the reports.
Strahan starred in and produced the short-lived 2009 Fox sitcom "Brothers."