The 'Real Girl' singer - who quit the girl group in 2005 to pursue a solo career - has filed an ownership request to the European Trademarks Authority.
Her legal firm Kilburn and Strode has confirmed the application has been registered but is yet to be approved. They are "hopeful" it will be passed in just a few months.
If the ownership request is granted Mutya would have the rights to use the Sugababes band name to sell a variety of products, including CDs, DVDs, T-shirts and books.
Keisha and Siobhan are named in the legal documents which have been filed, but have not joined Mutya in applying for ownership of the group's name.
The current Sugababes are currently preparing to release their new album 'Sweet 7' - which was re-recorded so Keisha's vocal parts could be replaced by Jade's.
Heidi - who is the longest serving member of the pop trio after replacing Siobhan in 2001 - previously claimed she and the girls would have no problem keeping the name because their record company Universal owns the rights.
She said: "Our record company owns the name so there are no conversations about who owns the name. I signed to Universal Records eight-and-a-half years ago with Mutya and Keisha, so we've still got the name."