The moves follow bus timetables being reduced this week by Lothian, Edinburgh’s main operator, and Lothian Country, which operates in West Lothian.
ScotRail and CalMac have also introduced service cuts for most of January.
A First Bus spokesperson said: “We’re currently looking at implementing a temporary reduced timetable from Monday 10 January across parts of our First Midland [which covers Falkirk/Stirling] and First West Lothian networks.
"We’re still finalising details on this but further information for customers will be available shortly.”
The operator told The Scotsman it had hoped to restore normal services in Glasgow after extending its normal reduced festive season timetable, introduced on Christmas Eve, from today to 10 January.
The spokesperson said: “We have been dealing with an increase in staff absences linked to Omicron, although the operation of the festive timetable did give us some headroom to absorb any effect on the network in terms of service cancellations.
"We had intended to revert back to normal timing from today, but increases in staff absence and self-isolation requirements have meant that we’re simply not able to ramp service levels back up.
"We’ve therefore extended the festive timetable to cover the rest of the working week this week (the equivalent of a Saturday timetable with some additional early morning trips on selected routes) to provide a better level of operational certainty to customers.
“We also anticipate that a Saturday service will need stay in play with additional early morning journeys on weekdays from 10 January until such time as our absence rate improves to a level that will support an improved frequency of service.”
The reductions involve services running at reduced frequencies, such as from ten to 12 minutes, and from 12 to 15 minutes.
First said changes to self-isolation rules announced by First Minister Nicola Sturgeon today would help the situation, “but it will take time to filter through before we see any positive impact from it”.
ScotRail, which has 421 staff absent today due to Covid, said more than half were due to testing positive for the virus rather than being close contacts of others who had contracted Covid.