The Kumasi-based side sit second on the log, two points behind leaders Aduana Stars, after sharing the spoils 1-1 with debutants Bolga All Stars last weekend. However, Lugarusic's men are well placed to challenge for a first league title since 2014.
Rising star Emmanuel Gyamfi, who has played under Michael Osei and Lugarusic at the Baba Yara, admits the latter has fostered the most powerful unity that can guide them to win the title.
"We are very happy this season and I think a lot have changed in our play. We were good last season but we look better this time around under Zdravko Lugarusic and hope to be the best," Gyamfi told Goal.
"There is unity among all the players than before and I believe this will help us win the title. We need to defeat Wafa on Wednesday and then prepare for the game against Hearts.
"It is my aim to lift it for the first time in my career," he added.
Kotoko are getting used to life without skipper Amos Frimpong, after the centre-back suffered a broken hand on opening day against Liberty Professionals, in his absence, Abeiku Ainooson, Ahmed Adams and Awudu Nafiu have done a wonderful job.
Wafa are ninth with eight points but midfielder Majeed Ashimeru wants his team-mates to pick valuable points to ensure that they do not find themselves in an unexpected difficulty during the final months of the campaign.
"We have started the season very well and need to continue picking points," Ashimeru said.
"We have to cement our status in the top-flight very early and then fight for a good position. We should not leave Kumasi without a point. I don't want to see us struggling with other clubs to avoid relegation," he added.
The two clubs have met eight times since Wafa qualified to the top-flight for the first time in 2005. Kotoko and Wafa have won three times each, with two games ending in a draw.
Wafa have failed to record a victory in their four trips to the Baba Yara Stadium, picking a goalless draw during the 2014-15 season but they have conceded five goals, scoring two in the process.
Wafa are without any major injury concerns but Kotoko have relatively few injury problems to contend with. Baba Mahama missed the last match due to a knock but could return against Wafa while defender Evans Quao is still in P.O.P.