Abraham, the younger brother of England and Roma star Tammy, played for the Saddlers in a training match at Birmingham City yesterday.
The 21-year-old is a free agent having left Fulham earlier this summer.
He spent the whole of last season at Newport, having been signed by Michael Flynn before the Welshman left the club in October and then joined the Saddlers as boss in February.
Abraham scored three goals in 17 appearances in all competitions for the Exiles, with most of his game time coming as a substitute.
He has also had loan spells at Scottish side Raith Rovers, Plymouth Argyle and Bristol Rovers.
Abraham may feature as Walsall host Villa in a pre-season friendly at Bescot on Saturday afternoon (1pm).