The first two stages of the East End Regeneration Route are in place around Oatlands, Polmadie and Celtic Park.
The 1.4km four-lane final stage will take it north to connect with Provan Road, south of the M8/M80.
Glasgow councillors will be asked on Thursday to release Â£250,000 of funding towards pre-tender work. Work could then begin in 2018 and finish in 2021.
Details of the project are outlined in a report which will go before councillors on Glasgow City Council's Executive Committee.
The reports states that a number of milestones - including compulsory land purchases - have already been completed.
It is argued that completion of the road will "assist both local economic growth and the creation of jobs".
The report states that it will help future housing development, bring vacant land back into use, reduce traffic on surrounding roads and improve noise and air quality.
Councillors are being asked to approve the final stages of a road in Glasgow connecting the M74 and M8 motorways.