But the struggling top-flight Kenyan club may have to fight off late interest from Rwandan bigwigs Rayon Sports, a team that recently parted ways with Brazilian coach Roberto Oliviera.
Mbungo has been out of work since his contract with another side Kiyovu SC ended in August. Before departing, he guided the team to a fourth-place finish during the 2017/2018 Rwandan league season, whilst also helping current Gor Mahia forward Francis Mustafa emerge among the top scorers with 13 goals.
The 48-year-old coach is also best remembered for nurturing current Gor Mahia and Rwanda national team striker Jacques Tuyisenge when the two worked together at Police FC in 2015.
His CV includes two domestic cups (Peace Cup) titles in his native Rwanda, plus a third-place finish at the 2015 Cecafa Kagame Cup. He has also managed AS Kigali in the Caf Confederation Cup and handled Rwanda's U-23 national team.
Should he opt for the Kenyan offer, Mbungo - who was linked with a similar move to AFC Leopards and Sofapaka earlier this year - will be assuming the hot seat at a club that has struggled during the 2018/2019 Kenyan Premier League season.
Under the tutelage of patron Gatundu MP Moses Kuria, the rebranded Mount Kenya United have lost all their three league matches this season, including an opening day 2-1 defeat to Sofapaka and 3-0 thrashing to Tusker last weekend.