"I felt I was playing well during the Six Nations even though I was out of position on the wing," Brown told Sky Sports News.
"I hadn't played there for a long time so I was always learning which is tough at that level given the quality of opposition. However, I can't look any further than Quins at the moment. What will be, will be - all I can do is get my head down and keep working hard.
"I would love to get that phone call. As a rugby fan since I was five, I've grown up watching the Lions so it would be a dream come true to be involved."
Brown has made 11 appearances for his country.