Lukjanciks is an England U17 international. His family has a Latvian background.
The Daily Mail reports, in addition to the Werkself, RB Leipzig, Olympique Marseille, Tottenham Hotspur, Aston Villa and Southampton are also interested in the 16-year-old.
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The goalkeeper is expected to reach the first team at Everton in the future.
Lukjanciks is a regular with Everton's U18 team.