Fly-half Sexton and flanker O'Brien have both recovered from calf injuries and should be available at Murrayfield.
Sexton was injured against Castres on 20 January but is said to be "feeling very positive" about his recovery.
However, uncapped Munster wing Andrew Conway has been ruled out after aggravating an existing groin problem.
Ireland playmaker Sexton has the chance to cement his starting spot, provided he comes through Tuesday's session.
Ulster's Paddy Jackson will start for Joe Schmidt's side if the Leinster star is ruled out while Munster's Ian Keatley has joined the squad as cover for the time being.
"Johnny's making good progress and he's back on track to train on Tuesday," said Ireland team manager Paul Dean.
"I think everything is fine, he's being very positive about it."
O'Brien has completed the rehabilitation on his calf issue and was expected to take full part in Monday afternoon's training session.
Full-back Rob Kearney says Ireland remain unfazed by his Leinster team-mate Sexton's latest quest for full fitness.
Sexton battled hamstring trouble before the turn of the year, with this calf problem proving yet another unwanted hurdle.
Kearney labelled injury doubts "par for the course" in any Test week, then tipped Sexton's understudy Jackson to thrive if pressed into service from the start in Scotland.
"We're all so used to it now," said Kearney, of general battles for fitness.
"On a weekly basis, more often than not, there's someone going in or out.
"Someone picks up a niggle or they're not fully fit, so the coach doesn't risk them. The way Test rugby is now, it's par for the course.
"Paddy [Jackson] has been there all last week running the plays. He's more than equipped and he's got a week head-start."
Ireland pair Jonathan Sexton and Sean O'Brien are set to resume full training after injury before Saturday's Six Nations opener against Scotland.