Tom Elliott and David McClarty UUP move
Former Ulster Unionist David McClarty has said he had been contacted by Tom Elliott about rejoining the party.
Mr McClarty was returned to the Assembly as an Independent after being de-selected by the UUP.
He said he told the party leader on Sunday night that he would not be rushed into making a decision
"When I make my decision I will take everything into consideration and do what is best not for me but for the people who elected me," he said.
"Coming back to the party was something I was asked to think about but there was no pressure from Tom (Elliott) and I told him I would make my decision later in the week."
The UUP are one MLA short of being able to claim two ministries in the new executive.
Alliance, which picked up eight seats in the assembly poll, is entitled to a ministry by right for the first time.
After his East Londonderry victory Mr McClarty described his treatment by the party as "shocking" but has since held what he described as "amicable talks" with the UUP party leader.
However Mr McClarty said they did not discuss the comments Mr Elliott made about Sinn Fein during the conversation.
UUP leader Tom Elliott had described Sinn Fein as 'scum' at an election count in Omagh.
Over the weekend Mr McClarty distanced himself from the comments and said that they were not indicative of the kind of "progressive unionism" he believed in.
In the last assembly, Alliance held the justice portfolio following a cross-community vote procedure introduced in the Hillsborough Agreement.
It has exactly half the total of seats on which the Ulster Unionists finished.
BBC Northern Ireland political editor Mark Devenport said that under the D'Hondt system, the UUP would get one department but when its turn came for a second pick, its seats would have half the value.
"So it's 8 versus 8. At this point the tie breaker is how many first preference votes each party received, with the UUP vote tally also being halved," he said.
"According to this method, Alliance is also ahead, so should take its first ministry before the UUP get a chance for a second."
Alliance leader Ford said using the D'Hondt system was not his preferred option.
He added: "I don't think it's a particularly proportional system. It's not my preferred choice but it's what the constitution says."