Force India are already well placed to record their most successful F1 campaign this year, sitting fifth in the constructors' standings, 32 points above Lotus, with three races to run.
"The appetite [for more] is there for sure," said Mallya, when asked by Formula1.com if fifth was the limit of his team's ambitions.
"If we finish the season in P5 it will already be our best season so far in the history of the team. [But] we are pushing the boundaries further every year.
"I always said the improvement has to be gradual. It cannot be as dramatic as other teams - the ‘big five' are constantly developing. And the whole sport is getting more competitive.
"When I started with Force India eight years ago, half a second [deficit] was okay - no big issue. Today half a second is a world apart. But we are doing superb for a team of our size."
Mallya said the team's form in 2015 offered added encouragement, particularly as they began the year with an interim car.
"Unfortunately we started late this year - our start of the season up to Silverstone was pretty weak until we introduced the B–spec car," he explained.
"Now this B-spec car is performing. Even in Austin, after a difficult weekend, Checo [Sergio Perez] managed to finish in P5."
Force India have improved their championship position almost year-on-year since entering the sport in 2008, when they finished 10th. Last year they secured sixth, matching their all-time best from 2011 and 2013.