After a review of the candidates, the IMF executive board aims to have decided on a candidate by March 3.
Lagarde, the former French finance minister who has overseen the IMF through the challenging eurozone bailouts.
She is widely respected in the global financial community but has not said directly that she wants to renew her position.
Asked about staying on at the annual IMF global meeting in Lima, Peru last October, she said: "I'm certainly open to the fact that it would not be my last annual meeting. But this is not for me to decide."
She already has the support of Britain.
Lagarde's renewal also faces a personal legal challenge: she could stand trial in France over her role in a banking scandal that predates her arrival at the IMF.
In December investigating judges placed her under formal investigation in the long-running affair of Bernard Tapie.
Tapie received a substantial state payout for his dispute with a state bank during her time as finance minister.
Lagarde has said she would fight the trial order, and the IMF executive board at the time reiterated its confidence in her.
Reports circulating in Paris yesterday indicate that the government here could support Ivory Coast-born French banker Tidjane Thiam
Lagarde easily won a contest with several developing country candidates to take over the IMF in 2011 as Europe was sinking deep into economic crisis.