Dalot spent last season on loan in Serie A at AC Milan and was tipped for a potential return to the Rossoneri this summer.
He is still at Manchester United after a move back to AC Milan did not materialise, but could yet make a move away from Old Trafford before the transfer window closes.
Dortmund, who sold Jadon Sancho to the Red Devils earlier this summer, are locked in talks to sign Dalot.
The Bundesliga side want to snap Dalot up on a loan deal which includes an option to sign him permanently next summer.
And they are pushing to get an agreement over the line in order to sign Dalot before the window closes next week.
Dalot has been an unused substitute in both of Manchester United’s Premier League games so far.
The former FC Porto talent has made a total of 35 appearances for Manchester United since he joined the club in 2018.