Still only 20, Tierney captained Scotland against Holland in Novermber before Charlie Mulgrew took the armband for the friendlies in March.
"I think myself, yes I would. But it's not up to me at all. It's up to the manager and his staff and whatever they think," Tierney replied when asked if he would take up the captaincy.
"I'm still a young boy - I'm 20-years-old. But I'm ready for any challenge."
However, Brown is still Tierney's club captain at Celtic and the fullback believes he can still learn from the midfielder.
"I think he (Brown) has said in one of his interviews he can see that happening. I'm obviously not going to say that, but just to captain the games I have has been a great honour.
"I'm just going to work hard and see where it takes me.
"He's a leader on every occasion. No matter what the game is, he'll give 100 per cent. He's Captain Fantastic, and for me - coming in as a young boy - there's no better role model.
"I think he's one of the most iconic captains this club's had and just to be here at the same time as him is an honour for me."