The 2-1 win over St Mirren ensures their bid to beat the drop goes on as they closed to within 10 points of the men from Paisley with four games remaining.
When asked if he would like the post permanently, Brown said: "Absolutely. Dundee is a big club. I had a great playing career here in my early years and the Dundee fans have always given us great backing. So I would love the opportunity.
"We had to win the game but overall we deserved it. These guys have been criticised all season and labelled First Division players.
"In the games that I have been in charge, they have proved that they are a match for every Premier League team we have played.
"Carl has had a hellish season with injuries but if we can get him sharpened up he is a big asset. He's been out for 11 months but it was a great finish.
"Everyone keeps writing us off but it's now out of our control. It's about what St Mirren do. But we've showed we're not a laughing stock."