Sea Containers has been warned that it must pay £143m to its two UK pension schemes if it wants to wind them up.
Bermuda, home of the insolvent Sea Containers
The UK pension regulator says it may issue the insolvent shipping company with a formal instruction to do this.
Sea Containers entered into the US Chapter 11 bankruptcy procedure last month, as it cannot repay bondholders.
The company says it wants to treat the pension schemes in line with its other creditors and is still in discussion with the UK regulator.
However, the regulator is worried that Sea Containers may try to avoid its legal responsibility to fund the schemes fully.
One scheme - known as the 1983 scheme - was closed to its existing members at the end of September.
That may lead to its being wound up.
The company would also like to close the second scheme - the 1990 scheme - as well to stop its deficit getting any bigger.
Together, they have about 1,300 members.
"I cannot say what will or will not be offered, but they will be treated as part of the insolvency process," said a Sea Containers spokeswoman.
The pension regulator has told Sea Containers that if its current negotiations are not satisfactory, it will issue the firm with a formal Financial Support Direction (FSD), which would compel it to follow the regulator's advice.
A spokeswoman for the regulator explained that an FSD was an anti-avoidance power.
"Were we to issue an FSD, we would have to think there was some act of avoidance there - it is an instruction to the company to make good the deficit," she said.
Since the regulator came into being last year, it has yet to issue an FSD to any employer.
If the company were to ignore it, the regulator would take legal action here and abroad to enforce its power.
Sea Containers owns the UK train operator GNER, but stressed that neither that company nor its own pension scheme was affected by its insolvency.