Both the President and François Hollande were attending a traditional dinner in honour of French jewish organisations, along with many other senior figures from French politics.
Hollande, accompanied by his partner Valérie Trierweiler, made the first move, crossing the packed room to get to the top table where the President was sitting.
Filmed by news cameras he was seen edging his way across the room until he tapped the President on the shoulder.
Slightly surprised, the President turned, smiled and stood up to shake hands.
BFM TV caught their brief discussion on film, which consisted of Hollande saying “I was asking myself why…..why all these people” to which Sarkozy replied “they’re not for me.”
After greeting some of the other guests at the table, Hollande then turned and left.
President Sarkozy is yet to declare his official candidacy in the poll which will take place in two rounds.
The first round of voting, in which voters can choose between all the declared candidates, will take place on Sunday April 22nd.
A poll for BFM TV on Thursday gave Hollande 30 percent of the vote, followed by Sarkozy with 26 percent. Just behind were Marine Le Pen of the far-right Front National on 17.5 percent and centrist François Bayrou on 13 percent.
The two leading candidates from the first round then go through to a final two-way contest on Sunday May 6th which, if the polls are right, will be between Hollande and Sarkozy.
The same poll gave Hollande 60 percent against 40 percent for Sarkozy.
President Sarkozy is expected to announce his candidacy in the next two weeks, according to a report by radio station Europe 1 on Thursday.