Fekir, who is now on World Cup duty with France, has caught the eye of several big clubs after an outstanding season with Lyon where he scored 21 goals in all competitions.
Bairner explained that the 24-year-old Frenchman will still depart Lyon for Anfield after the World Cup following the collapse of his move to Anfield before the tournament - which stemmed from concerns about a past knee injury.
'Nabil will be at Lyon next season I think, ' Aulas told RMC.
"I am working under the assumption that [Fekir] will stay with us".
Jurgen Klopp is now eyeing a move for his fellow countryman, Brandt, who was named in Germany's squad for the World Cup in Russian Federation ahead of Manchester Ciy's Leroy Sane.
Lyon president Jean-Michel Aulas is confident Nabil Fekir will remain at the club beyond this transfer window despite still being linked with a move to Liverpool and Real Madrid. If Nabil is here, it makes my job easier. "He is our captain and it is the coach's wish to keep him".
Bairner stated: "I've heard from two sources that a deal will most likely be done".
Before any transfer takes place Fekir will be hoping to help steer France into the World Cup Final, with a semi-final tie against Belgium next for Les Bleus.
Houssem Aouar has signed a new five-year contract with Lyon, the Ligue 1 club have confirmed.
Vettel wins British Grand Prix ahead of Hamilton
That was no comfort to Hamilton, who quickly worked his way through the back-runners as he posted the fastest lap times. Bottas, still on medium tires, was soon struggling, and Ferrari was celebrating when Raikkonen went past to go third.
England have the edge over Croatia, says Hamann
On Wednesday, it will be Croatia and England's turn, and both teams will appreciate what a massive opportunity this is for them. Cheryshev's four goals are tied with Belgium's Romelu Lukaku and Cristian Ronaldo for the second-most at the tournament.
Mastermind behind 1995 Japan sarin-gas attack executed
Two days after the attack police raided the compounds of the Aum Shinrikyo cult. "I've been in pain for years", he told AFP. Asahara guided the attack, according to testimony by his right-hand man, Yoshihiro Inoue, who also was executed Friday.
Tropical storm watch discontinued
Tropical Storm Chris is expected to bring swell and showers to Bermuda towards the middle of this week. The storm poses no threat to land, but forecasters expect it to become a hurricane on Monday.
Trump focused on Kavanaugh, Kethledge for Supreme Court
Senate Majority Leader Mitch McConnell, meanwhile, said he intends to hold hearings and vote on the president's pick this fall. He is a graduate of the University of MI , where he received both his Bachelor of Arts and Juris Doctorate degrees.