Centre Tuilagi has been pencilled in to return against Newcastle on April 27 after a scan revealed he had only strained his pectoral muscle in Leicester's 16-15 victory over Wasps last month.
"It should be a couple of weeks rather than months," O'Connor told British media.
"That's hugely positive. He (Tuilagi) is running around and is probably going to be into some team training late end of this week or early next week."
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"He (Youngs) has worked incredibly hard to get back, so that he can contribute at the back end of the season. All the indicators are that he should be in and around selection next week."
Young's return means he should be available for the England tour of South Africa in June. Tuilagi has not played for the national team for more than two years due to a string of injuries.
Leicester next face Bath at Twickenham on Saturday.
(Reporting by Hardik Vyas in Bengaluru; Editing by Peter Rutherford)
