The resolution will reportedly be put to the SNP party conference running across 27-28 April in Edinburgh.
Trident is Britain’s nuclear weapons deterrent and consists of four Vanguard-class submarines, which can carry up to 16 Trident II D5 ballistic missiles, each armed with up to eight nuclear warheads.
At any time, one submarine is on patrol, one is undergoing maintenance, one is preparing for patrol and one has just come off patrol and is recovering.
Trident is based at the Her Majesty’s Naval Base at Faslane.
A resolution put down by the Glasgow Maryhill and Springburn branch will be voted on at next month’s party conference.
In a statement run in The National newspaper, the resolution says: “Conference welcomes the continued support for nuclear disarmament and , with the impending inevitability of independence, we need to set out a clear timetable for removal of nuclear weapons from Scottish soil and waters.
“Conference believes that we need a practical description of the process and timescale to safely remove nuclear weapons at the very earliest opportunity on Scotland regaining our independence.”
The resolution adds: “Conference therefore agrees that we should develop a credible road map that has at its end point the removal of the Royal Navy’s nuclear armed and nuclear power submarine fleets from Scottish soil and the closure of related supported bases on Scottish soil.”
The nuclear base at Faslane costs the UK about £2.2 billion a year.
Nuclear weapons have been situated at the site for more than 50 years.
The scrapping of the Trident programme was a key platform in the 2014 Scottish independence referendum debate.