Australian half-back Connor Higgins will also join the Reds on a three-month trial from South Sydney Rabbitohs.
Foran, a half-back, is the younger brother of New Zealand international Kieran, made seven appearances for Manly last season.
The 24-year-old made his first grade debut for Melbourne back in May 2010.
Gleeson turned out for Salford in their pre-season friendly against Swinton earlier this month, following the end of his drugs ban.
Higgins, who has joined on trial, featured for South Sydney Juniors on their recent tour of the UK, which saw them take on BARLA Great Britain Lions.
The signings come following the confirmation of Dr Marwan Koukash’s takeover over the club.