O'Driscoll has yet to feature in Ireland's two Tests this summer - defeats to Scotland and France - because of a neck/shoulder injury.
But the Lions centre is nearing full fitness and could feature at the Aviva Stadium on Saturday.
He may be joined by centre Gordon D'Arcy and flanker Stephen Ferris, who have also spent the summer on the sidelines with respective ankle and knee injuries.
Wing Tommy Bowe, who is struggling with an ankle problem, should be in action against England a week later.
"Brian O'Driscoll, Stephen Ferris and Gordon D'Arcy are all continuing to progress well," said manager Paul McNaughton.
"It's expected that they will be upping their involvement in training this week and will be in contention for selection.
"Tommy Bowe is also making progress and it is hoped that he will be in line for selection the week after."
Full-back Rob Kearney limped off with a groin problem during the second half of Saturday's 19-12 defeat by France and his fitness is being monitored.
"Rob had a scan to examine the extent of the injury today and will be reviewed again tomorrow," said McNaughton.
"At the outset the injury does not seem too serious, but we will wait to see the result of the scan and also how the injury settles before we review it tomorrow.
"Outside of the normal bumps and minor knocks from a test match, there are no other major injuries to report."
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