It comes as the party continues to play its proverbial cards close to its chest over which ministries it will be targeting come the first plenary session on Thursday.
"Let us say that we have a good idea of exactly what we're going to do but, at this stage, it wouldn't be sensible to make that public," Mr McGuinness said.
Sinn Féin president Gerry Adams wouldn't be drawn on the issue either, saying: "There's very few negotiations are ever conducted publically and let's not change that tradition - there are lots of traditions we should change, but that's not one of them."
It is understood the DUP will aim for the coveted Finance portfolio with its first pick.
Sinn Féin may be reluctant to hand over Education, given the polar positions of the two main parties on the highly controversial issue of post-primary transfer - but the powerful position of Speaker is also highly sought after.
The DUP's Willie Hay held the post in the last term of the Assembly, after negotiations between the power-sharing parties.
It could well be next Monday before the Executive is in place. In the meantime, there will be a major negotiation in Stormont Castle.
UTV Political Editor Ken Reid, in his blog: Decision time
"I think Willie Hay did a very good job as Speaker - he was very fair to everybody and he found favour with a lot of people," Mr McGuinness said. "But there were some discussions between ourselves and the DUP about that position, about the prospect that we would alternate it - in the event that the electorate gave us the mandate to do so."
He maintains that, having again charged the DUP and Sinn Féin with the responsibility of leadership, the electorate has indeed given them that mandate.
"So we'll have a discussion with the DUP about that and I'm sure we'll come to a sensible arrangement," he added.
As for the other ministries, Mr Adams said: "We have a national officer board meeting of Sinn Fein this evening and we will feed in from this meeting to that. And we have an Ard Chomhairle meeting later in the week.
"So we will have very quickly a party view of what we want to do - but of course we have to do that in partnership with the other parties."
Over the issue of David McClarty's unique position, Mr McGuinness said: "I think that's basically between David McClarty and the people who elected him in East Derry and, of course, the party to which he had a previous allegiance.
"All I'm keen to see - and I'm sure Peter Robinson is exactly the same - is to get people into ministerial positions as quickly as possible and if possible to do it this week."
Mr McClarty, an ex-Ulster Unionist MLA, was elected as an Independent after being deselected by the party - he could now gift an extra ministerial post to either his former party or the Alliance Party, depending on whether or not he chooses to return to the UUP.
Amid the ongoing fallout from the Assembly election, Sinn Féin has also called for UUP leader Tom Elliot to withdraw his comments in which he referred to "the scum of Sinn Féin".
"Tom Elliott should not have said what he said - the people who he represents are not scum and the people who we represent are not scum," Mr Adams said.
"We have tried to be mature about this and give him space to withdraw those remarks and that's what he should - that would be the mannerly thing to do, just withdraw the remarks."