The veteran has been without a club since he saw his deal run out at the Magpies.
Per Chronicle Live, Dummett is the subject of an offer from Portsmouth for this season.
He is said to be mulling over the approach from the Championship outfit, and may join in the coming days.
Legendary former Newcastle and Pompey star John Beresford told Chronicle Live: "It'll be a very good move for him and for Portsmouth. What I liked about Portsmouth was the fans are very much like a northern crowd and are very intense. There's always a great atmosphere down there.
"Some clubs like Southampton and Bournemouth on the South Coast they are nice football clubs if you like! What was great at Pompey was the fanbase is brilliant and they make it hard for opposition. I had a great time at Portsmouth and they look like they are ready to take off again. My time there was great we just kept changing managers a lot.
"Portsmouth had a great FA Cup run when I was there in 1992 and of course they won it in 2008 so that's what the club is all about."