Sivasspor, knocked out of the Turkish Cup this week, lead Istanbul's Besiktas by just one point with 57 points and face third-placed Trabzonspor on Saturday.
Mid or low-ranked opponents then follow but the final game of the season will take Sivasspor to Istanbul to meet titleholders Galatasaray at home, currently with 51 points.
"Most people in Turkey are going for us. Obviously we are not one of the big Istanbul teams...and it would be great for the league if a team besides the big three won," Sivasspor goalkeeper Michael Petkovic told Reuters by phone.
"We are going into each game like its our last. We are giving it all our best," added the Australian.
The last non-Istanbul team to win the league was Trabzonspor in the 1983-1984 season. Only four teams have ever won the title: Fenerbahce, Galatasaray, Besiktas and Trabzonspor.
Sivasspor, who have led the league since late December and could qualify for the Champions League, were holding their nerve, the goalkeeper said.
"All the players are quite relaxed, we're still enjoying training every day, enjoying going out and winning."
Turks have been puzzling over the team's unexpected success for months, putting Sivasspor's winning form down to the influence of coach Bulent Uygun.
"He was a very good player in his time, he is still a young coach and understands what footballers think and knows what to say. He doesn't put too much pressure on us," said Petkovic.
"He has drawn a strong group of players -- we are not all superstars but we fight for each other."
Uygun, 37, has joked that Sivas, located in conservative Central Anatolia, offers little distractions for players, and as he knows the bars he is told as soon as a player buys alcohol.
Nicknamed "the soldier", Uygun has a website (www.bulentuygun.com) which includes poems he has written to Turkey's founder Mustapha Kemal Ataturk and rousing folk music.
"Actually if you compare us to the rest of the clubs in Turkey we are one of the most relaxed clubs in the league... We haven't got that military thing about us," said Petkovic.
Petkovic has modest expectations of the team's Champions League chances: "Just getting there would be a great achievement for us. It doesn't mean we have to win a game or win a point."
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