Guns and ammunition were found near Langfaulds Cemetery in Bearsden.
Police have confirmed that the cache was discovered in Baljaffray Road at 10.45pm on Sunday.
Glasgow gangster Kevin “Gerbil” Carroll, who was shot dead in Robroyston in January 2010, is buried in the graveyard.
A Police Scotland spokeswoman said forensic examinations were ongoing.
William Paterson (35) is serving a minimum of 22 years in prison for the murder of Carroll, 29, at an Asda car park.
A spokeswoman for Police Scotland said: “Around 10.45pm hours on Sunday, February 5, police recovered a quantity of firearms and ammunition from Baljaffray Road, near Langfaulds Cemetery in Bearsden.
“Inquiries, including forensic examinations, are currently ongoing in relation to this matter.”