Harewood had a spell in the Championship with Wolves last season, but he failed to impress Mick McCarthy enough to make the deal a permanent one.
The former Nottingham Forest and West Ham front man has never really secured his place in the first team squad at Villa Park since he joined from the Hammers in 2007.
Harewood, 30, was restricted to just six starts for Villa last season as he netted just one goal in 15 appearances.
Magpies boss Chris Hughton is eager to sign cover for crocked striker Shola Ameobi and Harewood, with his obvious strengh and speed, could be an ideal replacement.