The Parkhead chief hopes the game against Hearts today will produce a victory to mark another signpost on the road to overtaking Rangers and "becoming the best in Scotland".
Celtic, unbeaten in 17 league games, can cut the gap to just two points at the top of the Scottish Premier League by winning at Tynecastle in their remaining game in hand.
"We still have a long way to go to reach where I eventually want us to be," Burns said. "We are reaching out to be the best that we can be and that is still a long, long way off.
"The potential at this club is enormous, and we have made progress. Possibly we have got down the road quicker than we imagined. But the first step would definitely be to become the best in this country - that is the challenge in front of us.
"We are not kidding ourselves or wanting to run before we can walk by thinking about European ambitions. At the moment, Hearts is the only thing that concerns us and winning that match and keeping up our run of form."
Celtic are set to be unchanged after impressive away wins at Raith last Tuesday and Aberdeen on Sunday. Hearts were crushed 4-0 at Tynecastle and 3-1 at Celtic Park earlier in the season but Jim Jefferies' side are now full of confidence. "They have been playing well but we are only thinking about ourselves," Burns said.
Hearts have won four of their last five games, including three in a row for the first time in 15 months, and Jefferies is contemplating one change from the team which beat Falkirk on Saturday. Young defender Allan McManus, who at 21 has played barely a handful of games, could make way for ex- Ranger Dave McPherson. Paul Smith is also on stand-by for a midfield place.Reuse content