The 19-year-old looks set to move to Championship side Swansea City, after Sunderland accepted a bid of £2m for their Swedish forward earlier last week.
Sunderland look set to lose their striker and Jack Ross will be keen to bring in some attacking options, but the Black Cats should play hard ball and demand more than the £2m already agreed between themselves and the Welsh club.
Asoro ended last season with an excellent run of games, with the highlight of the youngster's season coming away to Fulham at Craven Cottage with a solo run ending with a goal from 25 yards. Sunderland lost the fixture 2-1 but Asoro's performance in South-West London sparked rumours of his exit.
The Stockholm born attacker has made 27 appearances in Sunderland's first team and has also had successful periods in the Under-23's.
The Swedish Under-21 player had even been previously linked to a number of top Premier League sides before Sunderland agreed to let the youngster go to Swansea.
However, despite Asoro being a name that top clubs are well aware of, the Black Cats are still keen to let the player go for a fee of £2m - which in the modern-day transfer market is a small fee for such a talented youngster.
New owner Stewart Donald suggested players wouldn't play for the club if they don't wish to do so, which could suggest Asoro lacked desire to play for Sunderland in the third tier of English football.
And Donald's desire to move players on in order for Sunderland to progress is certainly something that fans on Wearside have welcomed with open arms, especially given their recent history of players allegedly not always playing for the club for the right reasons.
With Asoro's imminent departure, Jack Ross will be keen to bring in a number of new faces which can help with any potential promotion bid next season.
And if Sunderland decide to hold off on allowing Swansea to buy Asoro for a bargain, extra transfer funds for the youngster can be put towards bolstering 42-year-old Ross's current squad for one of Sunderland's biggest ever seasons.