But rises will be pegged for commuters who have one of the new plastic smartcards.
Strathclyde Partnership for Transport (SPT) is expected to agree the new fares when it meets on Friday.
More than 6000 smartcards have been issued since the new ticketing system was introduced at the end of October.
Single journey prices will remain the same on smartcards, at £1.40 for an adult and 70p for a child.
People who opt to continue using paper tickets are facing steeper rises in their travel costs.
An adult single increases by 20p to £1.60, a return by 40p to £3 and an all-day ticket by 20p to £4.
Return tickets, which cost £2.60, are not available for people using the new plastic card.
Instead they can buy a new daily ticket, for £2.70, which allows them to travel as often as they like. It replaces the former all day ticket which cost £3.80.
The cost of a seven day adult ticket goes up by £1 to £13, with the cost of a 28-day ticket rising £5 to £50.
SPT has also introduced a new six-monthly ticket costing £250 for people with a smartcard and a 12-monthly ticket at £450.
The cost of a single concession fare rises by 10p to 90p, with a return going up 10p to £1.30.
Gordon Maclennan, SPT chief executive said: "SPT has spent the last few months introducing smart technology across the Subway.
"It replaces an out of date system that's been in use since the 1970s and was long overdue for replacement.
"It also included bringing in smartcards, with great travel benefits, and getting rid of inflexible paper tickets and unsustainable season products.
"The last time Subway fares changed was 18 months ago and the single journey price is being held at £1.40 on smartcards.
"Loyal customers will enjoy unlimited daily travel for only £2.70 which we believe still offers great value for money."
SPT says smartcard holders will be guaranteed the best prices available for Subway travel.
They will have access to season passes exclusive to them and can enjoy the benefits smart travel brings - less queuing, convenient use and free to join.
The concession price rise was agreed by the Strathclyde Concessionary Scheme members who administer it, in January this year and was due to be introduced in September.
SPT decided to delay introduction to allow smart technology to be fully introduced.
The decision to scrap 10 and 20 journey tickets infuriated many people who do not travel regularly on the Subway.
But a spokesman said: "The limitless validity period on 10 and 20 journey tickets was unsustainable both practically and financially.
"Smartcard customers can now use a pay as you go option which works in the same way as the old 10 and 20 journey tickets, albeit a slightly more expensive way to travel for infrequent trips,
"Smartcards do benefit those who use the system on a regular basis. The more you travel, the cheaper it is. "