National Coalition Party Prime Minister Jyrki Katainen was brief in comments Wednesday evening following talks on the issue with other party leaders.
"We are still in the midst of discussions. No decision has been made, but possibly tomorrow and Friday talks will continue and we'll see where we end up. There are differing positions," said Katainen.
The Social Democrats are keen for Finland to be involved in the planning of the tax which is supported by Germany and France. However, the National Coalition party says it would weaken the competitiveness of Finnish banks and harm employment.
EU finance ministers hope to proceed with the implementation of the transaction tax at their meeting next week. However, the project will not go ahead unless at least eight eurozone members sign up.
Some Finnish banks have already threatened to relocate outside the country if Finland signs up to the tax.