The 28-year-old has been a key figure for his club side so far this season, helping the Sundowns to beat Moroccan giants Wydad AC in the final of the African Football League.
Mudau has featured in four South African Premier Soccer League matches so far this term, with Mamelodi currently possessing a 100% record in the division after collecting 24 points from their opening eight contests.
The right-back has also appeared six times for his national side South Africa, scoring his first international goal during the 2-1 win over Benin in a CAF World Cup qualifier on Saturday.
According to South African news outlet SNL 24, Mudau is set for a move away from his homeland for the first time in his footballing career in the near future.
The report claims that Vincent Kompany's Burnley are interested in the right-back, who has made 101 appearances for the Sundowns since joining in September 2020.
Although it is believed that the Clarets are yet to make a formal approach for the six-time international, his form for club and country has attracted a number of potential European suitors.
Speaking to the South African Football Association earlier in the international break, Mudau explained how he would be open to switching to the Premier League and Turf Moor.
"Obviously, there are rumours here and there but I'm focusing on my team, which is Mamelodi Sundowns. But if an opportunity like that [playing for Burnley] can come, obviously I'll just take it," Mudau told his national side's media.
A move to Burnley would see the right-back link up with compatriot Lyle Foster, who joined Kompany's ranks in January from Belgian Pro League outfit Westerlo.
The 23-year-old has been the Clarets' leading marksman in the opening stages of the top-flight season, scoring three goals in seven games, however the striker is currently taking a break from football to receive mental health treatment.
With the former Orlando Pirates forward absent, Premier League veteran Jay Rodriguez has been handed more game time in the league in recent weeks, starting up front with Zeki Amdouni for the defeat at Arsenal last time out.
Unlike at left-back - where the failure to sign Ian Maatsen in the closing stages of the summer window has left Burnley short of options - the Clarets are well stocked in the right-back department, with Connor Roberts and Vitinho both capable of playing the position.
Madau will be looking to help South Africa to another victory as they travel to Rwanda for their second World Cup qualifier on Tuesday afternoon, with a maximum enough to extend their lead over section favourites Nigeria to four points.