The Celtic captain missed the Scots' opening two games against Serbia and Macedonia at Hampden with a hip problem which has needed careful management this season.
However, speaking ahead of the Hoops' Champions League Group G clash with Spartak Moscow tonight, Brown said: "Hopefully I can make the Scotland squad.
"I am feeling good just now, I have played four or five games in the last couple of weeks and everything feels good. So I think the rest has definitely done me good, that's for sure."
In a sometimes bizarre press conference in Moscow, Brown teased an enthusiastic local journalist who asked if the Celtic players watched the movie 'Braveheart' before games.
He said: "Yes, we watch Braveheart and we put our kilts on, just before we go out to warm up and we all dance together."
After a goalless draw in their first group game at home against Benfica, Brown is looking for Celtic to go one better against the Russian side.
He said: "I think we played well at home (against Benfica), I think we were unlucky that we didn't create as many chances as we would like to have done.
"We have got players in the team who can score – Kris Commons who is dangerous from 20 yards out, Gary Hooper is on form as well so hopefully we can take this into the game.
"We have had a few away victories in Europe this season and hopefully we can take that form into this game as well.
"But it is going to be hard, Spartak are a good team and we are going to have to play very well."