The 32-year-old midfielder on Monday morning called time on his Scotland career for a second time, having won 55 caps across two spells.
Tierney, 20, has played left-back, centre-back and right-back for Scotland and captained the Scots in the last fixture, a friendly against Holland at Pittodrie.
Rodgers said: “That will be up to Alex McLeish (to decide) but he is a player certainly for the future. It wouldn’t faze him.
“He has learned off Browny in his short time here in the first team.
“He now has over 100 appearances (to his name) and nothing fazes him, whether it is international football and playing out of position, he is exactly the same.
“He is certainly one who would be a credible successor to Browny if that’s what Alex chooses.”
Rodgers waxed lyrical about Brown, who reversed his initial decision to retire in August 2016 to help out then national manager Gordon Strachan, his former Hoops boss.
He said: “He has been a wonderful player for Scotland, a really inspirational captain.
“I spoke with him but it was purely his decision.
“The last time he stopped I think he had genuine intent to stop then but of course his loyalty to Gordon and to try to help the team brought him back and he played for a number of more games for him, which is the type of man he is.
“But now, given time and failure for qualification (for the 2018 World Cup) it has given him an opportunity to reflect where his career goes in its final years.
“And of course that means it is great news for Celtic because we have someone who is fresh and we will benefit from that.”