The 33-year-old is training with Pompey having recently been released by Championship side Doncaster.
He is a player well known to Portsmouth director of football Steve Coppell, who managed Harper at the Madejski Stadium.
Barker told The News: "James still lives in Reading so he's come in and is doing some work with us.
"If he comes in and is the best player every day, I dare say we'll look at doing something.
"Steve Coppell has said he's the fittest player he's had. You don't lose that overnight.
"James is a bit Marmite, really. He could maybe rub people up the wrong way. You either love him or hate him.
"If he's doing his talking on the pitch that's fine. He just loves playing football and is a fantastic person to have around."
- Sports & Recreation
- Steve Coppell