Heaslip missed the opening 26-3 win in Italy due to a shoulder injury and O'Brien pulled out after damaging his hamstring in the warm-up.
"Sean did an MRI scan last night which confirmed a hamstring strain on the minor end of the scale," Kearney told the Irish Rugby Union website.
"He is feeling good and we are hopeful that he will train with the squad tomorrow.
"If he comes through that, he will be available for selection. Whether that will happen or not, we will have to wait and see."
Best was taken off with a head injury early in the second half against the Italians but should have recovered in time to face the French on Saturday.
Flyhalf Jonny Sexton and prop Cian Healy are fully fit after recent problems.
"Cian Healy trained fully last week, including some scrummaging which he came through very well and he is available for selection," Kearney said.
"Jonny Sexton is cleared to train fully and again he is available for selection."
France beat Scotland 15-8 in their opening game of the tournament.
(Reporting by Ed Osmond; editing by Justin Palmer)
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