Robbie Henshaw could make an earlier than expected return to training this week but Johnny Sexton may miss Leinster's game against Toulouse.
Henshaw suffered his hamstring injury in the warm-up before Ireland's November game against Argentina.
The centre looked set to miss Ireland's Six Nations opener against England but Leinster coach Stuart Lancaster said on Monday that he may train on Tuesday.
Sexton is a doubt for Saturday's European game because of a leg injury.
Ireland, who clinched the Grand Slam last year, face England in their Six Nations opener in Dublin on 2 February.
Asked about Henshaw's fitness, Lancaster said the Ireland and Lions centre "is getting close".
"He's not going to train today but he's certainly moving along nicely," said the Leinster senior coach.
"If things go well today there's a good chance he could train tomorrow, which would put him in contention [for the Toulouse game]."
World player of the year Sexton did not train last week and is not expected to take part in Monday's session.
The defending European Champions are two points behind Toulouse in Pool A after the French outfit edged a 28-27 win when the teams met in October at Stade Ernest Wallon.