The Bosnian coach sparked speculation last month after he took a leave of absence ahead of Liverpool FC’s 1-0 loss to Chelsea FC at Stamford Bridge.
Buvac was linked with the Arsenal role following Arsene Wenger’s exit at the Emirates Stadium amid talk of a potential fallout with Jurgen Klopp.
The Reds were keen to play down talk of a bust up between Klopp and his long-standing assistant coach despite Buvavc missing the Champions League final.
Reporter Maddock shed light on the current situation at Liverpool FC involving Buvac and Klopp ahead of the new Premier League campaign.
Maddock wrote: “With the return of Pep Lijnders to Anfield, @LFC have made clear that Zeljko Buvac remains an employee of the club, and his position is unaffected by this coaching appointment. Jurgen Klopp still hoping Buvac will return following his absence for ‘personal reasons'”
The Reds lost 3-1 to La Liga giants Real Madrid in the Champions League final following goals from Karim Benzema and Gareth Bale.
However, Liverpool FC finished in fourth spot in the Premier League table ahead of Chelsea FC to ensure their continued participation in the Champions League.
The Merseyside outfit signed former Manchester United target Fabinho in a £40m deal from Ligue 1 side AS Monaco in the summer transfer window.
The Reds haven’t won the Premier League title but finished in second place in 2002, 2009 and 2014.
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