The Dutchman - who played for the Parkhead side between 1999 and 2004 - is in the sights of the Bishopbriggs club.
However it’s understand that any deal will depend on sponsors coming forward to fund it.
Petta, now 41, also had spells with Feyenoord, Ipswich Town and Fulham during his career but is best known for his stint at Celtic where he made over 50 appearances. most notably in the 6-2 Old Firm victory against Rangers in 2000.
After leaving Celtic he had spells at Darlington and Bradford City, as well as clubs in Australia, before retiring in 2009.
However rather than return to Holland he has remained based in Glasgow where he is a personal trainer.
‘Vale, under the guidance of ex-Partick Thistle and Stenhousemuir, are currently second in the Central First Division table and going for a second successive promotion which wouold take them into the Super League just five years after their formation.
They are also still in the Scottish Junior Cup - with a last 16 tie against former winners Hurlford United to come on Saturday, February 13.
And on Saturday they are also due to travel to Ayrshire to take on Cumnock in the West of Scotland Cup.