Erik Ten Hag's side are looking for a new man between the sticks after allowing Dean Henderson to join Nottingham Forest on a season-long loan deal.
That leaves veteran Tom Heaton as the only competition for first choice David De Gea, who has had a rocky start to the campaign.
Trapp helped Frankfurt win the Europa League last season, proving his worth in the penalty shootout win over Rangers in the final.
The former Paris Saint Germain goalkeeper is in his second spell with Frankfurt and is looking to be a part of Hansi Flick's Germany squad for the upcoming FIFA World Cup in Qatar.
Frankfurt have not enjoyed the best of starts to the season, losing 6-1 to Bayern Munich in their Bundesliga opener and suffering defeat to Real Madrid in the UEFA Super Cup but Trapp is not looking to jump ship yet.
Speaking to BILD, Trapp said: 'In the past few days, much has been reported about Manchester United's interest. It is correct that there is a written offer.
'Manchester United is a world club. I hope everyone can understand that I am dealing with such an offer and thinking about it.
'Yesterday I informed the responsible persons of both clubs that I had decided for Eintracht.
'I experienced sensational things here with Eintracht and we made history together. The start of the season was bumpy, but I have absolute confidence in us.'
