Both brands are using a similar image of a flying seagull for their logo.
However Gul's logo is trademark protected, whereas Hollister's is reportedly not, despite being prominently stamped and embroidered onto every Hollister product.
The Gul brand was established in 1967, while Hollister was launched in the US less than a decade ago in 2000, before expanding into Canada in 2006 and then the UK in late 2008.
A Gul spokesman confirmed that Gul was in dispute with Abercrombie & Fitch over the logo, but declined to go into further detail or to confirm a Daily Telegraph report that said it was seeking nearly £15m to allow Abercrombie & Fitch to use the logo.
Abercrombie & Fitch were not available for comment at the time of publication.
