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."

The former Chesterfield first team coach replaced Ashley Hoskin as manager in October 2015.
But the Seagulls managed four league wins under Lynch and are nine points from safety with eight games remaining.
"We thought he was the man for the job but unfortunately it didn't work out," Bay chairman Dave Titchiner said.
Captain Carl Rodgers and Luke Denson will be in charge for Thursday's home game against Mickleover Sports.
Colwyn Bay were relegated from the Conference North at the end of the 2014-15 season.

Both the Islamic State group (IS) and Kurdish militants have claimed a number of attacks in Turkey in recent months.
Turkey is part of the US-led coalition against IS, and coalition planes use its air base at Incirlik for raids in Iraq and Syria.
Turkey is also conducting a campaign against Kurdish militants.
How dangerous is Turkey's unrest?
Tears and destruction amid PKK crackdown
Turkey in midst of hideous vortex
A ceasefire between the government and the Kurdistan Workers Party (PKK) broke down last year.
On Saturday an emergency travel warning was published on the website of the US embassy in Turkey.
"There are credible threats to tourist areas, in particular to public squares and docks in Istanbul and Antalya. Please exercise extreme caution if you are in the vicinity of such areas," it read.
Antalya, on Turkey's Mediterranean coast, is a major tourist centre visited by millions of people every year.
The warning comes a day after Israel's counterterrorism bureau urged all Israelis to avoid Turkey, saying: "There are immediate risks of attacks being carried out in the country, and we stress the threat applies to all tourism sites in Turkey."
Ireland pair Jonathan Sexton and Sean O'Brien are set to resume full training after injury before Saturday's Six Nations opener against Scotland.
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Evo-Stik Northern Premier Division strugglers Colwyn Bay have sacked manager Kevin Lynch following Easter Monday's 3-0 home defeat to Marine.
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The US has warned its citizens of "credible threats" to tourist areas in Turkey, particularly in Istanbul and the southern resort city of Antalya.