Montebourg, who campaigned on a left-wing platform of protectionism and more state intervention, polled 17 percent of the votes in Sunday's vote.
François Hollande finished top with 39 percent of the votes and Martine Aubry in second place on 30 percent, with the two facing a final run-off to choose the nominee this Sunday.
Montebourg's score appeared to give him a king-maker role in the final vote and he had earlier promised to give his public backing to one of the two candidates.
On Thursday, his spokesman Géraud Guibert said he "will not be giving formal backing" because "he does not own his electors," according to newspaper Metro France.
Montebourg will decide whether or not to make public his own personal vote in Sunday's election.
However, the newspaper reported that there were still mixed signals from the Montebourg camp with another spokesman promising he would "make an announcement very soon" about his backing.
Montebourg wrote a letter to the two remaining candidates earlier in the week setting out what he would like to see them do. A statement from his camp said he would "not give an indication of his vote until the full process he has set out has run its course," suggesting he may still give one of the candidates his support depending on their final responses.
With just two days to go the candidates have been making final campaign tours and giving interviews to rally support. The eventual winner will represent the Socialist party in presidential elections due to be held in two rounds, on April 22nd and May 6th 2012.