Abbott revealed he is looking for a young goalkeeper to compete with number one Mark Gillespie at Brunton Park next season.
And the Cumbrians boss says he would not sign a player like Harper only to ask him to warm the bench.
"I think Steve Harper would be horrified if I said he was going to play second-fiddle to Mark Gillespie and spend another two years on the bench," he told the News & Star.
"If he is going to carry on playing, he will want to play, especially at a League One club. He has been a decent player and a top guy."