The Chapelizod Bridge or Anna Livia Bridge currently links the two areas but the bridge is very narrow and there is very little room for pedestrians.
The new bridge will create greater access to the Memorial Park and the rowing clubs that are located along the river.
The plan is to suspend the footbridges from the side of the existing Chapelizod Bridge in the same style as that of the boardwalk along the Liffey in the city centre.
The deadline for building firms to make a bid for the project is September 26 and construction should begin in the coming months.
"The bridge is a vital part of the project," said local Labour councillor Eric Byrne.
"It is a very hard site to enter."
"The Memorial Gardens are very seldom visited by anyone because they are so hard to visit," he said.
"Access to all the area is through a very awkward site from the North Circular Road."
The new pedestrian access is expected to make the open linear park along the Liffey at that spot easier to access. There are also plans to create lay-by areas off Con Colbert Road.
Four local authorities and the Office of Public Works are working to create the regional park with cycle and pedestrian paths along the 29km of the Liffey.
These will link a number of State-owned assets, including Memorial Park, Islandbridge; Farmleigh, Phoenix Park; Waterstown Park, Palmerstown; Lucan Demesne; St. Catherine's Park, Leixlip; Cooldrinagh Estate, Leixlip and Castletown House Demesne, Celbridge.
Planners at the OPW say such a project would be the envy of Europe, and would see the Liffey become a resource to be treasured.
However the difficulty with the project is that much of the Liffey Valley remains in private ownership, including land banks owned by developers.