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Wales face Marc Wilmots's side in a crucial Group B game in Cardiff on Friday.
Coleman's side are unbeaten in their qualifying campaign and are second on goal difference behind leaders Belgium.
"I'm as excited as I've ever been in my career, player or manager," Coleman told BBC Wales Sport. "I'm under more pressure than I've ever been as well."
Wales have not reached the finals of a major tournament since the 1958 World Cup in Sweden.
Coleman was a member of the Wales squad that came close to qualifying for the 1994 World Cup.
The former Fulham and Coventry manager was appointed national team boss in January 2012 following the death of Gary Speed.
Coleman lost his first four matches in charge, but has overseen a significant improvement since, with Wales reaching their highest-ever Fifa world ranking of 21st in May.
Friday's match at the Cardiff City Stadium will be played in front of a capacity crowd of 33,000, with all tickets sold within days of Wales' 3-0 win in Israel in March.
Coleman, who celebrated his 45th birthday on Wednesday, is comfortable with the expectations.
"Before we kicked a ball I wasn't going to play this campaign down," Coleman added.
"I sensed what we've got on the pitch and said as long as we got a little bit of luck in terms of injuries and suspensions, then something could happen in this campaign.
"I've never played it down from the start and I'm not going to play it down now."
You can watch the full interview with Chris Coleman in a special preview show on BBC Two Wales at 19:30 BST on Thursday, 11 June which will also be simulcast on BBC Radio Wales and streamed on the BBC Wales Sport website.
Manager Chris Coleman says Wales' Euro 2016 qualifier against Belgium is the biggest game of his life in football.