"Talks between the clubs could conclude on Friday about a deal that may amount to 60m euros", reported the BBC.More news: Elon Musk Says Tesla Will Not Make Electric Motorcycles
Fekir is due to undergo a Liverpool medical at Clairefontaine, the France national team's training base, before signing terms on Friday.
Liverpool want to wrap up the deal as quickly as possible and announce Fekir's arrival over the course of the weekend.
The 28-year-old has only featured in 18 matches for the Saints in the last two seasons and could join a long-list of former Southampton players who have joined the Merseyside club.More news: Ruthless Nadal breezes into last 16
"The transfer will certainly not close during the World Cup and I do not think there is any change before the World Cup", Aulas claimed.
Bayern Munich and Atlético Madrid have also been linked with Fekir, who can operate in a number of forward roles and would in effect be Philippe Coutinho's replacement at Anfield.
Aulas believes a pre-World Cup agreement may be the most profitable arrangement for Lyon after Didier Deschamps preferred Corentin Tolisso, Paul Pogba and N'Golo Kanté in midfield for France's most recent warm up match.More news: China warns USA no deal if tariffs go ahead