Bird's Singapore sprint race victory was his fifth of the season for Russian Time compared to Racing Engineering driver Leimer's three.
It left Mercedes Formula 1 protege Bird adamant he can overcome the Swiss driver in November's Abu Dhabi finale, where 44 points are still available.
"I'm pushing him, I'm pushing him," said Bird.
"We're where we want to be, we're right there fighting for the title until the last lap of the last race of the season."
Bird cited Saturday's feature race, when he battled back from a slow start and poor pitstop to finish eighth and seal reversed-grid pole, as a key part of his victory on Sunday.
"It was so, so vital," he added. "Sunday was the culmination of the hard work we put in on Saturday. I just did the same again and it paid off."
Leimer admitted that his Singapore sprint race had not gone according to plan.
"I was struggling in the race compared to the other guys, so I think I can be happy with the third place," he said.
"I'm still first into the last race. Sam is giving me a hard time, but that's really nice for the championship. We will see who wins in Abu Dhabi."
Felipe Nasr, Stefano Coletti and James Calado also still have remote mathematical chances of winning the title.