White spent last season on loan at Leeds, helping the Yorkshire club earn promotion back to the Premier League, before impressing with his parent club this term.
The Sun reports that Dortmund have now joined the race to seal his signature this summer.
Brighton value the 23-year-old at £35 million and turned down three offers from Leeds a year ago, the last of which came to £25m.
Dortmund have a good track record when it comes to picking up and improving young English talent, thanks to the recent success of Jadon Sancho and Jude Bellingham.
But the German side could face stiff competition for his signature, and United centre-back Harry Maguire is believed to have encouraged boss Ole Gunnar Solskjaer to bring White to Old Trafford.
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