The 19-year-old has already played for England at youth level but can still switch allegiances because he has yet to play for the senior side.
And Drogba took to social media after the on-loan Chelsea youngster opened his account at the same ground as the Ivorian did back in August 2004.
The 19-year-old scored 26 goals for a struggling Bristol City side last season, including 23 in the Championship, and he has once again been shipped out on loan by parent club Chelsea for the 2017-18 campaign.
Abraham, who earlier announced on Twitter that he had signed a five-year deal with his parent club, joins Swansea after the Welsh club beat fellow Premier League clubs Brighton and Newcastle to his signature.
The 19-year-old, who scored 26 goals on loan at Championship side Bristol City last season, announced his new deal on Twitter - although moments later the message was deleted
The Blues are said to be keen to tie down the young striker, who made a big impression during a stint in the Championship with Bristol City last season
The striker is on the wanted list of a number of clubs following a strong season with Bristol City and is expected to make an announcement once he returns from representing England at the ongoing under-21 European Championships.
Numerous clubs, including Newcastle United and Brighton & Hove Albion, have shown interest in the 19-year-old forward
Abraham scored 26 goals for Bristol City in the Sky Bet Championship last season and Swansea chairman Huw Jenkins says the Welsh
The England Under-21 international has been heavily linked with both Newcastle United and Brighton & Hove Albion
Brighton & Hove Albion are also said to be in the race to secure the forward's signature but according to The Sun, they could need to act fast with Newcastle holding discussions with Chelsea
Abraham is attracting attention with his performance
Abraham has spent the season on loan at Bristol City, and his 23 goals from 40 appearances in the Championship has led to numerous clubs allegedly competing for his signature next season
It was gathered that the Toffees have been eyeing the 19-year-old closely
Abraham is currently starring on-loan with Bristol City