Dolberg has been linked with a move to Manchester United this month.
The 19-year-old has emerged as one of Ajax's hottest prospects with his performances this season.
The Denmark international has bagged 11 goals from 27 appearances to fire Ajax up to second in the Eredivisie table.
He also made his international debut against Kazakhstan back in November.
Manchester United and Borussia Dortmund want to sign Kasper Dolberg
Kasper Dolberg has been compared to Zlatan Ibrahimovic
Football Manager 2017 wonderkids: 25 strikers you need to sign on FM17
Sat, November 5, 2016
Click through the gallery for a look at 25 wonderkid strikers you need to sign on Football Manager 2017
1 of 26
Click through the gallery for a look at 20 wonderkid strikers you need to sign on Football Manager 2017
His fine displays have not gone unnoticed with Jose Mourinho sending scouts to watch him ahead of a potential move to Old Trafford.
Get Quotes on Home Insurance
However, the Daily Mirror claim Borussia Dortmund are ready to rival United for his signature.
Dortmund are said to be prepared to sign Dolberg this month.
The Bundesliga giants are in need of a striker with Pierre-Emerick Aubameyang currently away at the Africa Cup of Nations.
Borussia Dortmund star Pierre-Emerick Aubameyang is currently away at AFCON
Adrian Ramos has also left the club on loan and looks set to move to the Chinese Super League at the end of the season.
Dolberg has drawn comparisons with United forward Zlatan Ibrahimovic during his time at Ajax.
The forward arrived in 2015 from Danish side Silkeborg for just £230,000 – but Ajax expect any potential suitors to match their £10million evaluation of the player.