McGhee, who has been deputy gaffer for three years, admitted: “I would argue that he’s been our best player since we have been here.
McGhee is confident Brown, 30, who made his international debut in 2005, still has a major appetite to represent Scotland as preparations begin for the 2018 World Cup qualifiers, which start in September.
The Scots have been drawn in a group with England, Slovakia, Slovenia, Lithuania and Malta.
McGhee added: “We are glad he is still around. This will be his 50th cap and he has got another 20 or 30 in him.
“I think the challenge he gets here is different from the challenge he gets at his club and he rises to it and he really enjoys it.
“I think with the England game, he will want to be part of that.”
Scotland face the Czech Republic in Prague on Thursday before taking on the Danes at Hampden a week tomorrow.