Asoro is currently working his way through the ranks at Brommapojkarna and recently made his debut for the under-17 side despite only just turning 15.
After an impressive performance, including two goals, Chelsea invited the fledgling to train with their youth team and will arrive in London on Sunday to showcase his skills to Jose Mourinho's coaching staff.
If Chelsea do manage to convince Asoro to join the club it will be a significant blow to their Premier League rivals Manchester United, who have had the player for four trials in recent months.
Brommapojkarna youth chief Tommy Soderstrom, who claims to have scouted for Manchester United in Scandinavia for 15-years confirmed interest from the Red Devils.
He told Fotbollskanalen.se: "Interest is high. I have worked as a scout for Manchester United for 15-years in Sweden and Finland so I have been with him over at United four times."
But although Manchester United and Chelsea have stepped up their interest in the youngster, a number of other clubs are still tracking his progress. Juventus, Manchester City, Everton, Aston Villa and Red Bull Salzburg are reportedly interested in hearing on the player's developments.
According to Soderstrom, youngsters in the past have chosen the leave early and hinted that Asoro is likely to follow the same path in the near future whether it be for Stamford Bridge or Old Trafford.
"John Guidetti chose the leave Brommapojkarna at age 16, while Albin Ekdal played one season with the first team before he moved," he said.
"We'll see what happens. There are various options."