The Scottish champions had bids for Doughty, who is into the final year of his contract at Charlton, rejected over the course of the international transfer window.
Charlton are desperate to keep hold of him, but Celtic are continuing to track the 20-year-old, who is admired by boss Neil Lennon.
Celtic could wait until next summer to make their move to tempt Doughty north of the border, when his Charlton deal expires, or look to lock down the midfielder to a pre-contractual agreement in January.
Doughty has made four appearances in League One for Charlton so far this season, with boss Lee Bowyer continuing to count on him.
He clocked the full 90 minutes in Charlton’s 0-0 draw against Sunderland before the international break and grabbed his first league goal of the campaign in the season opener, a 2-0 win at Crewe Alexandra.
Charlton have had a mixed start to the campaign, picking up four points from four games.
Doughty won the club’s Young Player of the Year award last season, with his performances catching the eye.