The German left-back is in hot demand this summer after turning out consistent performances for Augsburg in the last two years.
Max, 25, chipped in with four assists and four goals in the Bundesliga last season and Sport claim Liverpool and Barcelona are battling to sign him.
Augsburg are prepared to sell Max and have slapped a £18million asking price on their defender.
Max is under contract with Augsburg until 2022 and the German club will be hoping both Barcelona and Liverpool firm up their interest.
Liverpool are on the lookout for another left-back this summer after the departure of Alberto Moreno.