The champions have gone 22 games without defeat in the league since the start of the campaign and have not lost a goal in their last nine league matches as they stride towards another title.
Killie's best hopes of an upset - or even scoring a goal - probably lies with former Rangers and Middlesbrough hit-man Boyd, who was called into the Scotland squad for the first time in three years for the friendly in Norway last November due to an impressive return to form this season which has brought him 13 goals so far for the Rugby Park outfit.
And although the 30-year-old's scoring record against Celtic is poor - he has only notched once against the Parkhead side - Hoops manager Neil Lennon revealed his admiration for a player who has grabbed 211 goals in Scottish football, saying: "He has always been a very good footballer and you never lose that knack of scoring goals."
However, when Fisher was asked at the club's pre-match media conference about Boyd, he replied: "He's an okay player but we have got a good back-four."
When eyebrows were raised at his evaluation of one of the most prolific attackers in the Scottish game, the 19-year-old right-back remained nonplussed.
"He's all right," he said, before going on to speak about Killie and the increasing pressure on Celtic's domestic records.
"I have seen a bit of them because obviously Jacko (Jackson Irvine) is on loan there, so I speak to him a bit but I haven't seen that much of them.
"As long as the run keeps going it is going to get harder each game.
"We are aware of it and we have to be on our toes at all times.
"For Fraser (Forster) and the back four, we want to keep as many clean sheets as possible.
"It is a big target to go unbeaten and we have gone 22 games so far, so hopefully it can continue.
"We are not putting so much pressure on ourselves.
"The manager stresses to us that the league will take care of itself, and that we need to keep unbeaten, keep winning games and keeping clean sheets."
Englishman Fisher has Wales full-back Adam Matthews and Sweden defender Mikael Lustig blocking his way in to Lennon's side on a regular basis.
However, both are currently injured which allowed him to make his ninth appearance of the season in the 4-0 win over Hibernian at Easter Road on Sunday.
"It inspires me," he said. "It is good, it helps me, it is not intimidating, I can learn.
"You can talk to them and ask them certain things about the game.
"Both are very good full-backs. Adam is quicker and Mikael is good in the air.
"I get little bits from each of them and you try to put your own stamp on it and try to be better.
"I just wanted to play as much as possible this season. I didn't think I would play this much but I need to keep pushing.
"You don't know what is going to happen in football, especially here. I have to keep pushing and trying to learn."
Meanwhile, Celtic have complained to the Scottish Professional Football League after their home Scottish Premiership match against St Johnstone was rearranged with just over two weeks' notice.
The runaway league leaders were due to host the Saints on Saturday, February 15, with a 3pm kick-off.
However, the latest round of games selected for live television which were announced on Tuesday revealed that the match will now be played on Sunday, February 16 at 12.45pm.
The statement read: "Celtic Football Club would like to stress its disappointment with the most recent fixture change involving our match against St Johnstone FC.
"We apologise to our supporters for this late notice and the inconvenience this will undoubtedly cause.
"However, the matter is out of our control.
"We have made a complaint to the SPFL to record our disappointment regarding this issue and, going forward, we hope this situation can be improved to take greater account of the interests of supporters."
Elsewhere, St Mirren's home game with Aberdeen on February 15 has been brought forward to a 12.45pm kick-off on the same day.
Dundee United's game with Motherwell on February 22 has been moved forward by a day to the Friday night, with Hibernian's home match on March 1 against the Taysiders also being moved to the Friday.
Celtic's trip to Tynecastle to face Hearts on Saturday, February 22 will now kick-off at 12.45pm, as will East Fife's League One match with Rangers on Saturday, March 1.