The 28-year-old made his first start for United in over 10 months in their League Cup win over Newcastle United last week, having struggled with a chronic bowel problem.
"Obviously it's the manager's decision to pick me and he'll be looking at how much game time I've had for United. But I'm desperate to be involved. I was desperate to be involved in the Serbia and Macedonia games as well but it was just a little bit too early for me," he told the Daily Mail.
"I came up for the Serbia clash but United had a reserve game on Tuesday at the same time as the Macedonia match. I felt it would be better for me to get it under my belt. I wanted to be at Hampden, though. As captain of the squad you want to be there for the players, for the manager - you want to play your part."
Fletcher, who is still his country's captain, is expected to be named in Craig Levein's next international squad.