The Potters hope to fill in the area between the Seddon Stand and the Marston's Pedigree Stand to increase capacity to the 30,000 mark.
The work would concentrate on the area that currently accommodates the club's giant video screen with chief executive Tony Scholes saying the timing of their decision came with costs in the construction industry relatively low.
"The decision to apply for planning permission to expand the Britannia Stadium comes after careful consideration for a number of years," Scholes said.
"The atmosphere generated by our sell-out crowds since promotion to the Premier League has undoubtedly played a huge part in the Club's continued success and we have to be mindful of the fact that any expansion could have an effect on that.
"We have always said that we would be open to the possibility of expanding the stadium should we continue to remain in the Premier League and have the supporter base to fill it on a consistent basis.
"Home support levels are continuing to hold up very well as we enjoy our fifth season in the League and this was highlighted no more so than at our last home game with Queens Park Rangers.
"The attendance of 27,529 was our highest of the season so far and with the visitors only taking up the smaller allocation it shows that the continued interest of our fantastic support remains there."