Gomes made his senior debut for United in the final game of last season but has yet to sign professional terms with the club, with his current deal running out at the end of the season.
Barcelona have previously been reported to be interested in the 17-year-old, and haven't ruled out a move for him once his deal at Old Trafford runs out.
However, according to 'The Sun', the Catalan giants will face competition for the promising teenager's signature from German side Borussia Dortmund.
The Bundesliga outfit were reportedly very impressed with Gomes' performances during England's triumph in the U17 World Cup and are looking to snap the youngster up as he stalls on signing a new deal at Old Trafford.
It wouldn't be the first time Dortmund have done something similar, as this summer they signed highly-rated 17-year-old Jadon Sancho from Manchester City for a cut-price £10m deal.