The Ulster Unionist Party is expected to clarify its links with the Progressive Unionist Party next month.
David Ervine joined the Ulster Unionist group at the NI assembly
UUP deputy leader Danny Kennedy said an arrangement to allow PUP leader David Ervine to join the Ulster Unionist assembly grouping was "under review".
Some sources suggested a statement may coincide with the next report by the body monitoring paramilitary activity.
David Ford, Alliance, said the UUP was "backtracking" on a "grubby deal with representatives of paramilitaries".
The Ulster Unionists came under widespread pressure after allowing Mr Ervine to join their assembly group earlier this year.
The move was aimed at giving them an extra ministerial seat at Sinn Fein's expense if a power-sharing executive is formed.
The BBC has learned that the UUP may clarify its position early next month, around the time the Independent Monitoring Commission (IMC) releases a report on security normalisation.
Most of the September report will deal with police and Army activity but it will contain a general assessment of the threat posed by paramilitaries.
Another IMC report, due in October, will deal with paramilitary activity in more detail.
On Tuesday, Mr Kennedy, a Newry and Mourne assembly member, condemned a recent reported threat from loyalists to a newspaper reporter who has worked closely with the father of UVF murder victim Raymond McCord.
Mr Kennedy said the UUP has a political link with Mr Ervine "not an arrangement with the UVF".
He said his party opposed any threats or illegal actions.
Mr McCord senior was recently accompanied to a meeting with the Secretary of State, Peter Hain, by Ulster Unionist Lady Sylvia Hermon.
She is the UUP's only MP and has been a strong critic of the PUP link.
The Alliance leader, David Ford, has claimed the "Ulster Unionists are backtracking on their grubby deal with the representatives of loyalist paramilitaries."
Mr Ford claimed the Ulster Unionists were "finally realising that decent people do not want the representatives of armed and active paramilitaries being absorbed into their party."