Internacionale will retain the Texstyle World name if its revised bid for the troubled business is accepted.
Internacionale is understood to be the only company left interested in acquiring the whole business. Other potential buyers are looking at a break-up of Texstyle.
Internacionale chairman Ken Cairnduff said the Texstyle World stores would be relaunched, not converted to Internacionale's Au Naturale fascia.
'The opportunity is to run it on as it is, but with better product and a sharper image,' he said.
Au Naturale product will be introduced if his bid succeeds.