An announcement is expected within days that would see Tata separate its UK pension scheme from the businesses.
It could mean the potential merger between the company and the German steel producer, ThyssenKrupp is more likely to move forward.
The £15bn British Steel Pension Scheme (BSPS) has been a significant barrier to any agreement.
Tata has been in negotiations with pension regulators and trustees of the scheme.
A deal was done between unions and the company that would see reduced benefits for current employees, but the decision would affect all members of the pension scheme including those already retired.
Other similar pension agreements have seen the companies involved pay money into the fund as well as giving a stake in the ongoing business to the new pension providers.
About 6,250 people are employed by Tata Steel across Wales, including 3,500 in Port Talbot.
Tata Steel UK has offered to pay £550m into its now-closed pension scheme and give the fund a 33% stake in its UK business.
It means Tata would no longer have any responsibility for the pension scheme.
This pension arrangement is only available to companies that would not be able to continue trading without the change.
Who are ThyssenKrupp?
- Krupp's roots are in Germany more than 200 years ago and Thyssen was formed in the 1870s. The two steel companies merged in 1999
- The group employs 155,000 people in 80 countries across the world.
- The European steel division has 27,000 workers, producing 13 million tonnes of crude steel a year.
- There has been speculation about a merger with Tata Steel since last July.
Nearly three quarters of union members backed the new pensions deal earlier this year.
A Tata Steel spokesman said parties involved in pensions talks were in "positive discussions and we are hopeful of reaching a final agreement shortly".
The pensions regulator refused to be drawn on any speculation. It said progress was being made and an official announcement would be made in due course.
A spokesperson for the steel trade unions said: "If accurate, we welcome this development which will lead to certainty for scheme members following a year of unprecedented turmoil.
"Our members will now expect the trustees to provide all the information necessary to enable them to make the right decision for them and their families."
Pensions expert Stuart Price, partner with Quantum Advisory, said a deal has been done with a new pension scheme being set up, with better benefits than a "worse case scenario" of members relying on the safety net of the pension protection fund (PPF).
"Tata Steel will continue to sponsor the scheme and will stand behind it and pay in more money if needed to keep the scheme well funded," he said.
"Going forward, members will be worse off than if the British Steel pension scheme had stayed in place but it's better than the alternative with the PPF."