The Bundesliga club face the prospect of selling Jude Bellingham at the end of the season with several clubs across Europe interested in a deal for the England international.
Dortmund have also confirmed that Mahmoud Dahoud will leave the club on a free transfer when his contract expires at the end of the season, which also heightens their need for a new central midfielder.
According to Sky Germany, Gallagher is on Dortmund’s shortlist ahead of the summer transfer window, although the German side have not made an approach to Chelsea.
The report claims that Chelsea could possibly be open to selling Gallagher due to their inflated squad, while a transfer fee of around €50 million (£44.2m) is anticipated.
The 23-year-old had struggled to secure a regular in the team under Graham Potter but has started three of Chelsea’s four matches under Frank Lampard.
He was also singled out for praise by Lampard following Chelsea’s 2-1 defeat at home to Brighton earlier this month.
However, Gallagher will continue to face strong competition for a place at Chelsea.
Speaking at his press conference on Tuesday, Lampard described Enzo Fernandez, who Chelsea signed in a €121m (£106.8m) deal from Benfica in January, as ‘the future’ of the club.
‘I think he’s a fantastic talent. I think for a young player to have achieved what he has achieved in this footballing year has been amazing,’ Lampard said.
‘To be part of a World Cup-winning team, to earn himself a move to the Premier League and a club like Chelsea.
‘I agree maybe it’s a difficult moment to come to the club. He’s been at the club a few months and it’s been a difficult time, which has been a challenge for him. It’s a challenge that will make him better because everybody will put a lot of eyes on his performance, give him a lot of responsibility.
‘The reality, at his age coming here, he also needs support and help and those things. Those things can take time, speaking the language for instance. I think he’s a fantastic talent and he is the future of Chelsea, one of, central to a lot of it.
‘We must also give him that time to settle because will have happened to him very quickly. I really like Enzo, I’ve been very impressed.’
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