Liverpool confirmed they have agreed terms with the Burnley forward, whose contract expires this month, but a fee between the clubs is yet to be established.
Ings, who will complete the move on July 1, had been the subject of interest from Tottenham but has opted to join Liverpool, where McAteer feels the striker may have to bide his time.
“I think he only got about 10 or 11 goals the season before this one but being in the Premier League has meant his all-round game has come on,” McAteer, who played for Liverpool between 1995 and 1999, told Sky Sports News HQ.
“His workrate is fantastic and he’s been the shining light in a disappointing season for Burnley. Everyone has been to watch him and it’s Liverpool that have taken the plunge to bring him to the club.
“Potentially he’s another one of those signings that isn’t going to play straight away, he’s not a marquee signing and he is going to need bedding in for a period.
“He is a quality signing and one for the future.”