Both Premier League sides have also reportedly held talks with Demirbay's agent and said they are willing to meet his release clause, per Sport Bild's report (via Andy Ha of Football.London).
A Turkey international at youth level, Demirbay opted to represent Germany as a senior international and scored in his only appearance as the world champions won the Confederations Cup in Russia last year.
He is an attack-minded central midfielder and has been a key player in Julian Nagelsmann's Hoffenheim side since joining the club in June 2016.
This season he has played in 15 of Hoffenheim's 21 Bundesliga matches, netting two goals and providing one assist.
However, the No. 10 lasted just 17 minutes of Saturday's clash with Hertha Berlin before he was substituted with a knee injury that is likely to keep him sidelined for "the foreseeable future," per the Bundesliga's official website.
A fully fit Demirbay could be an exciting addition to either Liverpool or Arsenal, as he is a talented attacker who boasts confidence on the ball.
Given the market, he would also be a relatively cheap attacking purchase at £28 million.
However, he is arguably not the kind of midfielder either Arsenal or Liverpool need.
Both clubs have a number of talented attacking options. Demirbay would likely find it hard to unseat Sadio Mane, Mohamed Salah or Roberto Firmino at Anfield, while Arsenal have Mesut Ozil and Henrikh Mkhitaryan in their squad, both of whom prefer the No. 10 role.
On the other hand, the Gunners and the Reds are both sorely lacking in the defensive-midfield department and should arguably be channelling their funds towards making a telling addition in the deep-lying central area.