A Bayrou challenge would likely deal a blow to Macron, another centrist who is among the leaders, but whose campaign has lost momentum in recent days.
If the veteran politician decides not to run, both Macron and conservative Francois Fillon will hope to benefit in their close-fought contest for a place in the second round, almost certainly against far-right leader Marine Le Pen.
Bayrou, a 65-year-old former education minister, has though already ruled out backing Fillon and could rally behind Macron.
Bayrou has said he will give his decision at around 1630 local time (1530 GMT) at the headquarters of his political movement MoDem in Paris.
Polls show Fillon, a former conservative prime minister, and Macron, an ex-investment banker and economy minister, battling neck-and-neck for second place in the April 23 first round of voting.
The latest survey on Wednesday showed little change in the pattern. Le Pen leads first round voting intentions with 26 percent of support, with Macron in second place on 22 percent slightly ahead of Fillon on 21 percent.
Either man would beat Le Pen in the second round - a trend confirmed by Wednesday`s Opinionway poll - although she has been narrowing the deficit in recent surveys.
Both Le Pen and Fillon are embroiled in financial scandals.
Le Pen has denied allegations by OLAF, the European Union anti-fraud agency, that she gave parliamentary assistants fake jobs paid for out of EU funds.
French judges opened a fraud investigation on Dec. 15 after prosecutors handed the dossier over to them following a preliminary investigation of more than a year.
POLICE QUESTION LE PEN ENTOURAGE
On Wednesday, French judicial police questioned Le Pen`s bodyguard, Thierry Legier, and her chief of staff, Catherine Griset, in relation to the probe.
Le Pen`s lawyer, Marcel Ceccaldi told Reuters that the affair was a "manipulation" aimed at destabilizing the party`s election campaign. Le Pen has denied any wrongdoing.
Fillon, meanwhile, faces an investigation into allegations that his wife did no real work for the hundreds of thousands of euros in taxpayers` money she was paid in past years. He has said she carried out genuine work for him.
The affair initially knocked support for Fillon but polls suggest he has recovered ground in recent days.
Le Pen on Wednesday drew a distinction between the probe against her and the fraud investigation against her rival, saying: "The French can tell the difference between genuine scandals and political dirty-tricks."
Earlier on Wednesday, Francois de Rugy, who stood unsuccessfully as an ecology candidate in the primaries of the left that elected Socialist Benoit Hamon as candidate, said he would back Macron for the presidency.
De Rugy won 3.82 percent of the vote in those January primaries, and has been critical of Hamon`s policies.
"I want to take part in the renewal of politics that Emmanuel Macron has launched," he said on France Info radio.
Environmentalist politics are split in France.
Greens party candidate Yannick Jadot, who is standing for the presidency himself and whom polls show picking up between 1 and 2 percent of the vote, is in talks with Hamon about an electoral pact under which Jadot would withdraw in Hamon`s favor.
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