The 26-year-old’s future at Atletico Madrid looks set to be a hot topic heading into the summer transfer window.
Several reports have suggested that Barcelona and Arsenal are both increasingly keen on signing Alvarez in a deal that could exceed £100 million.
According to ESPN journalist Jorge Baravalle, however, Chelsea are working hard behind the scenes to bring Alvarez to Stamford Bridge.
Baravalle said: “I insist, people are talking about a lot with Barcelona and Arsenal. But I’m being told that the team slowly moving forward is Chelsea. Chelsea, quietly, are advancing for Julián Álvarez.
“I’m told there are conversations. In fact, part of the agency handling Julián’s transfer was in London this week, watching Chelsea v Arsenal.
“They know both clubs want him, but what I’m being told is that, as of today, the most advanced contacts are with Chelsea.”