Officials are in talks about replacing the policy with a new way of enhancing education.
Pawit Thongroj, an adviser to Education Minister Chaturon Chaisang, says he will suggest to the minister that the provision of tablets to students in Prathom and Mathayom 1 classes ends.
A "smart classroom" using technology to enhance teaching and learning in schools could be introduced instead, the adviser said.
The smart classroom would be equipped with about 30 tablet computers, a smart board, server and class-management software.
The smart classroom would make better use of the state's education budget and avoid procurement problems such as those encountered with the free-tablet policy, said Mr Pawit, one of the Pheu Thai Party's education policy experts.
Although students will not have their own personal device, they will be able to make use of what the smart classroom has to offer.
The smart classroom will enable teachers to monitor their students' use of technology and allay concerns about young students surfing age-inappropriate content.
Mr Pawit said tablet distribution had entered its second year and data on the scheme is being collected and analysed.
The tablet policy, which was introduced in 2012, delivered about 800,000 tablet computers to all Prathom 1 students. The second phase last year was extended to cover Mathayom 1 students.
The number of delivered tablets so far is 1.6 million units, worth over 4.6 billion baht.
Procurement of more tablets is currently in progress, even though many students have been waiting for their new tablets for more than a month.