United, though, are said to be drafting up a shortlist of other potential candidates for the role, with Frank said to be a name under consideration.
The Dane has enjoyed a hugely successful spell with Brentford since achieving promotion to the top flight in 2021 and currently has the Bees sitting ninth in the table.
Known for his tactical flexibility and skilful handling of the media, his appointment would represent a departure from the usual big names brought in to manage at Old Trafford.
Frank, however, insisted he is still very happy with his current role in South West London and is not looking to move on any time soon.
‘It is a delicate question. I have a big responsibility to Brentford, the fans, players and staff,’ he told reporters on Monday.
‘We will focus on Sheffield Wednesday [in the Carabao Cup on Tuesday]. I am very happy here it’s one of the best clubs in the world. What happens in the future, who knows
‘I will repeat myself. I’m very happy here and can see myself being here for a long time. If something comes up, let’s see. Now? No. Very happy.’
Asked for his thoughts on the departure of Ten Hag, Frank added: ‘Of course I feel for Erik. He is a great coach and has a great career. He did a good job at Man United, two trophies in two years.
‘It’s a non-stop developing football world and that [record] is more than acceptable. At these big clubs, there are massive expectations but I also think there has to be a reality check. Clearly on paper, there are three clubs at the top of the table are in a better place [City Arsenal and Liverpool].
‘When you are a head coach yourself, You always feel for guys who lose their jobs and I’m sure Erik gave everything.
‘There are better people to judge that [improvement]. He had a very good first season and had more than a few injury problems that doesn’t help.’