The daily newspaper states that the Merseyside rivals are set to go head-to-head in a race to secure Erkin after Inter withdrew their interest.
However, the Turkish international has not received any offers as of yet according to his agent Batur Altiparmak.
Altiparmak told Turkish-football.com: “There have been no offers.”
“There have been enquiries from 5-6 teams but I have not mentioned names of any clubs and no agreements have been reached either.”
The Toffees reportedly sent scouts to the Turkey v Austria international which was played on 29 March which Erkin started in.
In fact Wolfsburg, Werder Bremen, Everton, Juventus, Cologne, Inter Milan, Stoke City, Schalke, Sunderland, Mönchengladbach, Bayern Munich, Olympique Marseille, Stuttgart, Leicester and Leverkusen will all send scouts to watch the game at the Happel Stadium according to the official Salzburg website.
Turkey won the game 2-1 at the Ernst-Happel stadium extending their unbeaten run to 13 games.
The 27-year-old also started in the 2-1 win over Sweden at the Antalya Arena stadium last weekend.