Injured Irish trio expected to face France
They are expected to take part in a full training session on Tuesday.
Sexton has been sidelined for Ireland's first two Six Nations matches against Scotland and Italy due to a calf injury.
Kearney has struggled with a biceps problem and Murray sat out training last Friday with an adductor issue.
But team manager Paul Dean tipped the British and Irish Lions flyhalf Sexton to use Tuesday's training session to show he can face the French in Dublin.
"Johnny Sexton will play a part in training today [Monday], but will fully train tomorrow. Hopefully when he comes through that, he'll be fine for the weekend.
"Rob Kearney continues to make progress. He'll do some contact work today and he'll fully train tomorrow.
"If you talk to Johnny and Rob they'll both say that they're 100 percent fit and ready to go, so we just need the medics to pass them and they need to prove to us that they are.
"Conor Murray's workload was managed in Monaghan last week. It was a difficult week for the players last week, but I'm happy to report that the outlook is positive."
Ireland, who also expect flanker Peter O'Mahony to return after hamstring concerns, narrowly lost their Six Nations opener against Scotland and then thrashed Italy in Rome.
Agence France-Presse