U.S. financial regulators are wrapping up work on a proposal that would ease restrictions around relationships banks can have with companies like hedge funds and private equity funds, according to a top bank regulator.

A new proposal simplifying the rules around how banks invest in those so-called "covered funds" is expected to come in the first quarter of 2020, according to U.S. Comptroller Joseph Otting.

Otting told reporters that the five regulators charged with implementing the "Volcker Rule," a post-crisis rule aimed at curbing risky activity by banks, have struck an agreement on the upcoming proposal, which could be unveiled in weeks.

"There is unity amongst the five regulatory agencies on this topic," he said on Wednesday.

The proposal is expected to wrap up years of work by the Trump administration to ease restrictions around the rule, which Wall Street has lobbied to curtail since its creation in 2010.

In August, regulators voted to ease rules policing riskier trading by banks under the rule, giving firms more leeway and simplifying requirements for permitted trading activity.

At the time, regulators said they planned to propose further Volcker simplification on the "covered funds" portion of the rule sometime in the future.

The Office of the Comptroller of the Currency, the Federal Reserve, the Federal Deposit Insurance Corporation, the Securities and Exchange Commission and the Commodity Futures Trading Commission share responsibility for the rule.

Those rules are aimed at limiting the exposure traditional banks have to riskier financial firms, but banks have complained that the limits are overly restrictive and can prevent them from investing in new ventures.

Otting did not detail what could come in the upcoming proposal, but the Treasury Department recommended in 2017 that the requirement be drastically simplified and give banks more leeway in their investment options.