The increase means a rise of 20p – that's almost 17% – for a single ticket and 20p – just over 8% – for a return.
Strathclyde Partnership for Transport, which runs the network, said passenger numbers had dropped and the increase was necessary to keep the public subsidy from councils to a minimum.
The news come 24 hours after it was announced Scots commuters and travellers face a 4.2% rise in rail fares. That will likely take effect from January.
But if the Subway proposals are approved this week, the price rise will come into effect on September 10.
SPT wants the Subway fares to go up from £1.20 to £1.40 for a single ticket and from £2.40 to £2.60 for a return.
The transport agency defended the planned rise by stating the Subway was still cheaper than a bus journey for similar distances and that prices had been held for three years in a time when bus and rail fares increased 12%.
The overall increase is 9% but for a single ticket, which accounts for 43% of all tickets, sold the rise will be 16.6%.
Latest available figures show the Subway has lost around 120,000 passenger journeys in the last year, with the biggest monthly drops recorded over the busy shopping period of November and December.
SPT executives expect difficult economic times to hit Subway numbers further. They say fares need to rise to maintain income levels.
Eric Stewart, SPT assistant chief executive, laid out the plans in a report to Glasgow councillors.
He said: "It is recognised Subway patronage and revenues may be impacted by the current economic climate and while the impact is difficult to predict, it is vital the Subway ticketing and fares offering has the flexibility to stimulate growth."
The review, he said, had assessed fares in comparison with local bus and rail fares and it was believed the Subway was still better value, with bus journeys costing up to £1.85 single.
SPT chief executive Gordon Maclennan said: "Subway fares have remained static for three years. Over the same period, rail and bus prices have risen 12%.
"The proposed increase is well below that and we believe the Subway is still one of the cheapest and most efficient ways to travel."
Fares on subsidised bus routes will also go up 5% and MyBus or Dial A Bus fares will increase from £2 to £2.50.
SNP councillors fear the Subway fares rise may deter even more people from using the service.
Malcolm Balfour, SNP Councillor and SPT Partnership member, said: "The proposed increase in Subway fears has the potential to put passengers off using the service.
"Although perceived as only a 9% increase across the board, in real terms it is a 17% rise on the single adult fare at a time when the public are already finding it hard to make ends meet.
"In comparison rail fares are going up only 1% above inflation.
"I am concerned the Subway fares increase will have an adverse effect on the people who use the system on a regular basis and also on visitors to this city in the run-up to the Commonwealth Games in 2014.
"I call on SPT to review this increase, or at least consider phasing it over the time."