The Sun says the 17-year-old is stalling on a new deal, with United fearing he could be poached.
An Old Trafford source said: “There is chatter around the club that Dortmund are the latest side in for Gomes.
"He is pals with Jadon Sancho and that could be something that tips the scales on whether he stays or goes."
There are fears at United that Gomes could also tempted by Spanish giants Barcelona.
Last season he became the youngest player to appear for the Red Devils first team since Duncan Edwards.