A number of Catholic and Church of England schools are understood to be in the scheme, including St Paul's RC primary in West Derby.
It is not compulsory, but some parents believe it improves pupils' safety as they would not need to bring cash to school and risk being bullied for it. It also speeds up queues, and experts say a cashless system would stop pupils buying junk food.
No-one from the school was available to comment, but one parent said: "To me, the electronic scanning of seven-year-old children's thumbs is not in their best interests.
"About a month ago, we were first told a new cashless system would be coming into operation.
"If you really do not want your child's thumb scanned, they can input a six-digit number instead. So why use the thumb print at all?
"The previous system worked well for years, so I cannot think of a valid reason to introduce this."
Liverpool council has no plans to introduce the equipment.
Cllr Paul Clein, executive member for education, said: "I do have misgivings about it and it is something that parents should have to actively agree to.
"Any attempt by schools to force children to take part is wrong, and I would be very concerned if it became part of entry criteria, for example.
"I suppose it is a reflection of the times we live in, but I do not know where we draw the line."