The 62-year-old Israeli met officials from the club yesterday and he looks set for his 12th management post.
"I have completed the meeting with officials of Levski Sofia and I can say I am 99 per cent certain that a deal will be reached in the next days," Grant told Ghanasoccernet.com.
"There are just some few points to be ironed out but I am sure that we can complete the deal for me to coach the club with so much promise.
"I am returning to London this afternoon and I am sure I will join the club if everything goes to plan over the next few days."