The 27-time champions are exploring stadium-sharing options next season with clubs in Aarau and Emmen.
Club officials say the city has refused to reduce annual rent at Letzigrund stadium of 870,000 Swiss francs ($900,000) and a 500,000 Swiss francs ($515,000) bill for game-day policing.
Grasshoppers have shared Letzigrund with rival FC Zurich since the venue was renovated to host games during the 2008 European Championship.
It was promised a stadium to replace its former Hardturm home but the project stalled over legal and planning disputes.
Grasshoppers last won the league in 2003.