The England international looks odds-on to leave Stamford Bridge this summer and has been linked to a whole host of new teams.
talkSPORT understands that Brighton have recently entered the race for the midfielder, and now Sky Germany claim Dortmund are also keen.
They also report that he is on the list of replacements for Real Madrid signing Bellingham and new Brighton recruit Mahmoud Dahoud, but his price is likely to be prohibitive.
Rated at as much as £50million by some outlets, Gallagher is one of the players Chelsea are looking to raise funds from and thin down their bloated squad.
But the 23-year-old recently reaffirmed his commitment to the west London club saying: "I'm a Chelsea player and I love Chelsea.
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"It's been a really tough season for me and the whole team and club. We'll work as hard as we can to get Chelsea back to where they belong."
Gallagher's price is likely to be lifted by reported interest from Tottenham and Chelsea, but BVB have some spare cash after selling Bellingham for £88.5m, rising to £115m.
The Bundesliga runners-up have had huge success with English recruits, having previously sold Jadon Sancho to Manchester United for £73m, and new starlet Jamie Bynoe-Gittens looks like he's on his way to the top.
But they're also interested in English-produced talent too, with United academy star Hannibal Mejbri also of interest according to the Manchester Evening News.
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After five first team appearances and a goal, he spent last season on loan at Birmingham, the club where Bellingham was also picked up from.
Now the Tunisian is attracting interest from his impressive Championship stint, with an offer of €15m [£13m] being considered.