Kenny to hold talks on new Cabinet
Talks over the next day or so at Government Buildings are expected to focus on the direction of the coalition with the Social Protection Minister having already stated her priority is to match social repair with economic revival.
Ms Burton has also indicated she would like to remain in her portfolio.
Elsewhere, it is expected Labour will take on the jobs and enterprise ministry while the futures of party veterans Eamon Gilmore and Pat Rabbitte are unclear on the back of the departure of another member of the old guard, Ruairi Quinn.
Alan Kelly, appointed deputy Labour leader on Friday, is widely expected to earn a promotion to cabinet.
Ahead of the talks, Ms Burton said: "I think we both want the Government to continue its mandate and we want to chart a pathway to, basically, a better Ireland.
"We have seen a very promising report this morning in the form of a pre-budget submission from (business lobby) Ibec which acknowledges there is very solid growth and recovery in the economy.
"I think the job of us as leaders of respective parties is to get that to work for everybody and all the respective parts of Ireland."
Unsurprisingly, the Taoiseach would not be drawn on weekend speculation about new ministers where he said 10 different cabinets had been suggested.
"What the people want is a government that is working in the interests of the country, we've come a long way, as I say, to build on those foundations, and for those reasons I'm really looking forward to discussing that future agenda with the Tanaiste," Mr Kenny said.
The full list of new ministers is not expected to be known until Wednesday.
Other major questions to be decided will include where the foreign affairs portfolio goes, whether Environment Minister Phil Hogan will remain in government or take a vacant European Commissioner role, and if the Taoiseach will keep an ally in the troubled, big-budget health ministry.
The first round of discussions were pencilled in for mid-morning with policy matters expected to dominate the agenda before the two leaders get around to put names on seats.
Ms Burton set out her stall in her opening speech following the Labour leadership contest.
In it she referred to the single goal of improving living standards for all and stated that one of her first priorities was to set up an independent body to advise on the level of the minimum wage, a Low Pay Commission.