The Potters are keen to progress after a period of stability since winning promotion to the Premier League in 2008, and hoping their proposal will be well received by local authorities.
City initially intend to fill in the south-east corner, currently occupied by the giant stadium video screen, although further redevelopments haven't been ruled out if attendances continue to grow.
"The decision to apply for planning permission to expand the Britannia Stadium comes after careful consideration for a number of years," said chief executive Tony Scholes.
"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 club are currently undertaking £6million-worth of developments at their Clayton Wood Training Ground to comply with the category one status granted to the academy earlier this year.