Victory over St Johnstone at Parkhead on Wednesday night will take the Hoops nine points clear of Aberdeen at the top of the Scottish Premiership ahead of a William Hill Scottish Cup quarter-final and Scottish League Cup final against Dundee United later this month.
The Norwegian targeted the treble, a feat achieved only by Martin O’Neill (2001) and Jock Stein (1967, 1969), when he took over from Neil Lennon last summer.
With his side now playing at the top of their game following a tricky start to his tenure - they passed up two chances to get out of the Champions League qualifiers - the Celtic manager has moved from hope to expectation.
“I think we are the best team,” he said.
“If we don’t get to our full potential then I will be disappointed but the cup is the cup.
“You can get a red card, or be very unlucky but if the performance is bad and we lose because we are not good enough then I will be a little bit disappointed because I believe we can do it.
“I didn’t say we were going to win the Europa League because that was not realistic but it is realistic to win the treble.
“I know that it is up to us. If we don’t do it then we are not good enough but high goals gets high demands and good performances and this group can handle it.”
The former Stromsgodset boss stressed, however, that he would not deem it a failure if he missed out on all three trophies.
He said: “You can’t say that because then I would put too many demands on our players.
“This is a big, big chance, the players can make history.
“The players have done so many things, played in the Champions League and won the league but no players have won the treble.
“We have a real chance now so we just have to keep focused.”
After an arduous week, Deila joked about a novel way to prepare for the visit of the Perth side.
The Scottish champions were knocked out of the Europa League by Inter Milan in the San Siro last Thursday night before arriving back in the early hours of Friday morning and the Hoops players had to dig deep into their energy reserves to overcome 4-0 Aberdeen on Sunday.
“What we have worked on is lying on the couch more so they have the rest,” he said
“They were very tired after the game.
“Aberdeen were fresh and had the belief that they could beat us. The players felt heavy-legged but as the goals came so did the energy and by the end we were running over them.
“It is a very important game against St Johnstone. If we lose that game the game at the weekend is almost nothing.
“So it is important that we get a good result.”
Defender Efe Ambrose admits it is the best chance for a treble since he joined Celtic from FC Ashdod in 2012 but he remains cautious.
The 26-year-old NIgeria international said: “I want to give it our all to see if we can do it. I feel it’s our year. “It’s not going to be an easy task as we’ve got a lot of games before then.
“You can’t say we’re going to win every game because you never know but we need to keep believing we can.”
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