The Real Madrid forward has netted three times at the finals in France - making him his country's top scorer at major tournaments - and it was his cross that forced Gareth McAuley's own goal in the last-16 victory over Northern Ireland.
Bale also scored the only goal of the game when these sides met in qualifying last June, with Wales following up a 0-0 away draw with a 1-0 victory in Cardiff that helped propel them into the finals.
But Wilmots, who wants his own players to display some of the ruthlessness which saw them put four past Hungary in the last round, says dealing with Bale is a collective responsibility.
"We know Wales very well," he said, as quoted by Euro 2016's official website. "They have made a great evolution and have two top players in their team: [Aaron] Ramsey and Bale.
"We lost one time in the qualification by an individual mistake. But then we also had plenty of chances ourselves.
"Bale is playing in a free role and is a bit everywhere, on the wing, and in the central attack. But I will not put one marker on him, we will collectively deal with him."
Wales, who have kept two consecutive clean sheets for the first time in their tournament history, last reached this stage of a major competition at the World Cup in 1958, where they were beaten by Brazil.
Belgium, meanwhile, made the last eight at the World Cup two years ago and are now chasing their first semi-final place since the tournament in Mexico in 1986.
After falling to a 2-0 opening defeat to Italy, Wilmots' side have recaptured some of their best form, scoring eight times without conceding in their last three matches - thanks largely to the impact of captain Eden Hazard, who will be returning to the city where he made his professional debut.
Swansea City defender Neil Taylor, who is used to facing the Chelsea forward in the Premier League, is aware of the challenge Wales face in keeping Belgium nullified, but he is confident that they can produce another surprise in a tournament which has seen a number of shocks to date.
"We expect a different game to Northern Ireland," he told Euro 2016's website. "Belgium are a very, very good team coming into form at the right time.
"We're all very excited, we're in the quarter-final and it's massive. When you get to the quarter-finals you expect to perform quite well. People will expect them to win, but a lot of results in this tournament haven't been expected."
Thomas Vermaelen is suspended for the clash at Stade Pierre-Mauroy - a ground located just 10 kilometres west of Belgium, and which will host its final match at Euro 2016 on Friday.
Hazard is battling a thigh problem but Wilmots expects him to be fully fit, while Coleman hopes to have captain Ashley Williams available despite a shoulder injury.
A number of players are a booking away from sitting out a potential semi-final: Ben Davies, Aaron Ramsey, Taylor, Sam Vokes, Jan Vertonghen, Thomas Meunier, Axel Witsel, Marouane Fellaini and Michy Batshuayi will all miss the next round if they collect a yellow card.
Key Opta Stats:
- Wales only had one shot on target in their last game against Northern Ireland, it was from a Gareth Bale free-kick.- Injury time included, Wales have trailed for only two minutes and 31 seconds in total over their first four games at Euro 2016.- All three goals conceded by Wales at Euro 2016 have come from the 56th minute onwards. They've also all been scored by substitutes.- Seven of Belgium's eight goals at Euro 2016 have been scored after half-time, including six in the last half-hour.- Kevin De Bruyne has been directly involved in 12 goals in his last 12 games with Belgium (five goals, seven assists). He's the last Belgian player to score against Wales, back in October 2013 (1-1).- The top European assist providers at the last two major tournaments combined (World Cup 2014, Euro 2016) are both Belgian: Kevin De Bruyne and Eden Hazard (five assists each in total).- Hazard has scored/assisted four of Belgium's last six goals at Euro 2016. He completed 12 dribbles against Hungary on Sunday, the most in a Euros game (since 1980).