The 25-year-old attacker has a year left to run on his contract but wants a return to his Birmingham roots, seeing a move to Kiddy where ex-Iron man Mark Jackson is captain as ideal.
Watkiss has already added ex-Rochdale defenders Wayne Evans and Daryl Burgess who will bring vast experience to the squad along with veteran midfielder Martin O'Connor and young prospect Laurie Wilson from Burton.
Watkiss said of Sheldon: "He is a player that we like and someone we are interested in.
"A winger has been a problem position for us and we are looking to address that.
"Gareth is a local lad and we will shall see what will happen."
Also taking a trial at the Conference club is released former Iron YTS midfielder Russ Penn.
Sheldon has had a three-year spell at St James' Park since leaving United three years ago and has played for the English National XI side, a non-league representation of the English national team.
The player made almost 100 appearances during his time at the Iron, most famously scoring the two goals that took United to Wembley in the 1999 playoff semi-final.
He also set up Alex Calvo-Garcia's famous goal at the Twin Towers.