Alan Thompson will regard winning this season's Clydesdale Bank Premier League as the equal of anything he has achieved in his career, but last night the Celtic coach admitted it was annoying to hear references to a "tainted title".

Thompson and the rest of manager Neil Lennon's backroom staff will celebrate a championship if Celtic avoid defeat at Kilmarnock today. They established their credentials with a 27-game unbeaten run in all domestic games between October and March, and sit 18 points clear of Rangers with only six matches left. If Celtic won all their remaining games their points total, 96, would be the highest by any Premier League champions in the past eight years.

However, former Rangers striker Mark Hateley described Celtic's impending victory as a tainted title on the grounds that the Ibrox club had been crippled by its 10-point deduction for going into administration, effectively knocking them out of a two-horse race. Thompson dismissed that disparaging description but said it was irritating to hear it. "Tainted titles? Absolutely no chance," he said. "We were 15 points behind Rangers and we turned that deficit around. Regardless of the 10-point deduction we'd still be eight points ahead at the minute and in pole position. It will not be tainted for us. It might be for others . . ."

An army of 15,000 Celtic supporters will descend on Rugby Park for today's noon kick-off, filling three of the stadium's four stands in expectation that their team will get the point required to become champions for the first time since 2008. That they will do so at some point, either today or in any of their remaining handful of matches, is a formality. The certainty of becoming champions has given the run-in a slightly unreal feel, devoid of tension, but Thompson praised those players who had proven their superiority over Rangers and everyone else over the course of Lennon's second full season in charge.

Thompson did part of Lennon's work for him yesterday by sitting in for the manager at the club's usual Friday media briefing. Lennon has temporarily removed himself from press duties having been irritated by some coverage of his half-time exchange with referee Calum Murray at last month's Old Firm game. Even so, Lennon's life, happily, is calmer and less troubled than it was a year ago when he was one of the victims of a grotesque parcel bombing campaign. Almost exactly a year ago, Thompson fulfilled the Friday media duties because a suspect device had been intercepted on its way to Celtic. The mental strength Lennon showed in dealing with that, before taking the club to the brink of this championship win, had made him more impressive than ever in Thompson's opinion.

"I think everyone is so pleased for Neil: players, staff, everyone," he said. "If it happens tomorrow then great. We will all celebrate it with him because he deserves it. He has been through a lot. He puts in an awful lot of hard work that people don't see, whether it is going to games, watching players or going to watch kids coming through the system at Celtic."

There will be vindication, too, for Thompson and fellow coaches Johan Mjallby and Garry Parker who were described as inexperienced when there was talk of Celtic appointing a "mentor" – perhaps Stuart Baxter or Gordon Strachan – to help Lennon. "We were always positive about doing the job and having the knowledge to do the job," said Thompson. "When things like that are you said you think 'well, why, we are capable of doing it'. I think we've shown that."

No discussion of the imminent title is complete without reference to the day they seemed on course to implode, and maybe even lose their manager, at the ground where they could wrap it all up. On October 15 they were 3-0 down at Kilmarnock with more than 70 minutes gone before dramatically rallying to draw. Lennon later admitted that at half-time, three goals down, the thought of offering his resignation had flashed through his mind. "It might have been accepted, it might not have been, we'll never know," said Thompson. What had Lennon said to him at the time? "I was nearly f****** walking there . . . "

Instead of resignation point it was a turning point. Within hours of salvaging a draw that afternoon Rangers were held surprisingly at home to St Mirren, so no ground was lost. "I was going back to Newcastle with my dad after the Kilmarnock game and we stopped at a garden centre in Carlisle. After the coffee my dad said 'Rangers have dropped points' and I thought 'this could be a turning point'. From then on it just kept turning."