The band are playing at Manchester Arena on September 18, but the LTA wants Great Britain's Davis Cup tennis tie to be held at the venue.
Great Britain's semi-final against Australia is scheduled for September 18-20, reported BBC.
LTA chief executive Michael Downey spoke to Florence + the Machine's agent but couldn't convince the band to put tennis ahead of music.
Great Britain are now expected to host the tie in Glasgow instead.
Florence + the Machine's "How Big Tour" also includes shows in Belfast, Dublin, Sheffield, Glasgow, Newcastle, Nottingham and Birmingham.