The band own the rights to the use of the term worldwide, including live performances and records.
The management company for Dion, who has sold more than 140 million records world-wide, offered to buy the rights for $50,000 (£32,000) but the offer was rejected by the band. 
They fear its use would jeopardise their chances of cracking the US market.
The band told the firm they didn't want to appear to be "Celine Dion's support act".
But the management company are pressing ahead with plans to use the title anyway, prompting the band to consider suing the singer.
'Backing band'
The firm told Muse: "Our client will proceed without the proposed settlement and will use the mark Celine Dion Muse for its shows and related goods and services."
The band's lead singer Matthew Bellamy said: "We fully intend to crack America with our next album and we don't want to turn up there with people thinking we're Celine Dion's backing band.
"I find her music completely offensive for a start and I'm sure our fans do as well. 
"They've now told us they are pressing ahead with the Muse name whether we like it or not - they think if we try and sue them they will crush us with their might."
Dion will appear in Las Vegas in March, at a brand-new 4,000-seat theatre at the Caesar's Palace casino, designed to resemble the Colosseum in Rome.
The concert is scheduled to run for a minimum of three years with tickets costing up to $1,000.
Muse, from Devon, have released two albums, Showbiz and Origin of Symmetry, selling about three million records worldwide.
