With home games against St Mirren and Ross County either side of a short trip to Partick Thistle next midweek, they can get over the line without leaving the city.
Even before the ribbons are placed on the trophy, though, the Hoops are setting their sights on next season's Treble.
And Adam Matthews revealed watching Aberdeen lift the League Cup at Parkhead has served only to whet their appetite to clean up domestically next term.
But the Welsh full-back believes they have to get the balance right to achieve a clean sweep, something they have failed to do this time around.
The Hoops have not lost at home in the league since going down 1-0 to Inverness in November, 2012.
Matthews wants to see that form replicated across the board and said: "We wanted to win every competition we were in this season.
"We are disappointed with the way we played in the cups but our league form has been brilliant and we want to keep that going to the end.
"Last season we did really well in the cups, but I think that hindered our league form.
"It has obviously switched around this year.
"Hopefully, next season we can put the two together and win every competition we are in."
The planning for the next campaign has already begun. But Matthews knows they still have business to complete, and is eager to get the title sewn up.
Celtic are 24 points ahead of second-placed Aberdeen and the defender said: "We want to do it as quickly as possible.
"We just have to keep focusing on what we are doing. We can't worry about what Aberdeen are doing.
"It's three games and they are a big three games.
"We want to keep playing the way we are playing. In the second half against Kilmarnock, we were really good, and we want to take that into Saturday's game against St Mirren."
Liam Henderson will again be in contention to play in front of Matthews and the 22-year-old has been impressed by what the kid, five years his junior, has brought to the team.
Matthews believes the midfielder can follow the path blazed by another Academy graduate, James Forrest.
He said: "Liam has shown all season in training he's a top player and he didn't look out of place at all when he played against Kilmarnock.
"For a debut, it was among the best I've seen.
"He's a totally different player from James. But technically he is up there with the best in the squad, not just the young ones.
"He has the potential to be as successful as James."