The 25-year-old left-back moved signed for the Canaries in the summer on a free transfer from Rangers but failed to settle and moved back to the SPL in January on loan until the end of the season.
"Steven has been playing very well so hopefully we will be able to do something to keep him," Brown told the Norwich Evening News. "It will all depend on what Norwich want to do with him."
Smith added: "It's never been about money for me. I'm not going to stay at a club if I'm not enjoying it.
"My aim is to play 30-35 games a season. I don't want to get to the end of my career with people saying I only played a few games here and there.
"I'm enjoying my time at Pittodrie, probably more than at any time in my career."
Source: PA
Source: PA