The move is just one of several waste and recycling options considered by the council on Thursday.
Black bags are currently collected fortnightly.
The council's head of environment, Richard Brown said there will be "high public interest" whatever they come up with.
A report before the policy scrutiny committee outlined the challenges faced by the council's waste service as a result of funding pressures.
It said Â£1.2m needed to be saved over the next four years. This is in addition to potential fines for missing statutory performance targets.
Five options were presented to the committee. They looked at what was being collected, how often and by what means.
Options for black bin bag collection were weekly, fortnightly and three-weekly, while limiting the number of customer-provided sacks to two or three.
Pembrokeshire council  stopped supplying residents with free black bags in 2016.
The report also outlined an opportunity to save money by working with Ceredigion council, which faces "many of the same challenges".
The committee's comments will be reported to Pembrokeshire council's cabinet before a decision is made.
Mr Brown said waste services "was the one service we all have a vested interest in" and that they have to "do the best they can" and "look at future change".
Black bin bags could be collected every three weeks in Pembrokeshire as the council looks to meet "severe budget cuts" and performance targets.