The defending Guinness Premiership and EDF Energy Cup champions attract capacity crowds for home games at Welford Road and have been investigating ways of increasing capacity and improving facilities at the city centre stadium.
Chairman Peter Tom said: "We want to make sure that everyone who wants to watch the Tigers can get into the stadium. We have sold-out our home fixtures in league and cup for the last three seasons.
"This year we have taken the capacity at Welford Road up to nearly 17,500 but the Board have been working closely with the City Council and other parties in looking at ways of improving the stadium and its facilities.
"The decision has now been taken to apply for planning consent from Leicester City Council."
The first phase of the redevelopment scheme is to replace the Next Stand with a new 10,000 capacity stand, taking the stadium capacity up to around 24,000. Subject to planning approval, Tigers would hope to start work in Spring next year with the first phase.
There are a number of options available in terms of the building timetable but this cannot be confirmed until a decision is made on the scheme by the planning authorities and the contractors.