One bookmaker has the Parkhead club at 1/40 to make it three title wins in a row.
Ahead of the curtain raiser against Ross County at tea-time, the Scotland international was asked how the players felt about the perceived inevitability of another championship victory.
He said: "I think it maybe adds more pressure on to the players. But we have handled that in the past and I'm sure we can handle that again.
"A lot of SPFL teams have good squads this season and just look at St Johnstone doing well in the Europa League on Thursday (1-0 win away to FC Minsk), so I think it will be harder this season.
"We have signed a few new players and the squad is looking really strong just now.
"We still have a few players to come back from injury and once we do, we will be looking good."
Manager Neil Lennon is looking for more consistency from his players in the league this season.
He said: "I would imagine we would be heavy favourites (to win the league) but there has to be improvement on our domestic form from last year.
"The first part of the season we were a bit iffy at home and very good away and in the second half of the season we were brilliant at home and very iffy away.
"We lost seven games and I want a big improvement on that.
"We scored a lot of goals. Our goals for was very good, our goals against was down a little bit on the previous two seasons.
"You are always looking at areas where you can improve and at statistics and obviously we would like to get our points haul back up to the mid-80s to 90s."
Ross County manager Derek Adams is hoping his side can transplant last season's good home form against Celtic down to the east end of Glasgow today.
In their three meetings against the champions in Dingwall, County beat Neil Lennon's side 3-2 and drew 1-1 twice.
However, their trip to Parkhead saw them convincingly beaten 4-0.
Adams said: "They have taken in a £3million signing this week (Derk Boerrigter) but from our point of view, we hope to do well and hopefully cause an upset.
"We are away from home and Celtic Park is a terrific venue to play football.
"We played well at home, can we do that away from home? We will go and try."