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Allende had two spells with Arsenal in 2016 and Arsene Wenger wants to look at him again, according to football.london.
The 17-year-old attacking midfielder is thought to have a promising future and has been dubbed the new Alexis Sanchez.
Allende started his career at Cobreloa, the same club where Sanchez made his professional debut in 2005.
He rose to prominence in 2015, starring for Chile at the under-17 World Cup.
He captained his side and scored two goals in the tournament.
After impressing he then moved to Deportes Santa Cruz in 2016 and has made 22 league appearances for the Chilean second division side.
Allende is attracting attention from several other European clubs, including Shakhtar Donetsk.
Arsenal fans will hope Allende would play with Sanchez if he signed and not replace him.
Sanchez’s contract at Arsenal runs out at the end of next season and there is no word of an extension just yet.