Speculation has also linked the powerful 23-year-old with Chelsea, Arsenal and Lyon.
Annan was an integral part of the Ghana side which reached the quarter-finals of this summer's World Cup.
According to his agent, Lars Petter Fosdahl, Annan is wanted by a host of top clubs.
"There is interest from a few countries, and a few big clubs. It is a big ask moving from Norway to a top Premier League club, but people have succeeded in the past despite it being a massive task," Fosdahl told sport.co.uk.
Fosdahl cites the example of another of his clients, Mame Biram Diouf, who moved to Old Trafford and scored his first Premier League goal for the Red Devils against Burnley in January.
"It was only a year ago when Mame Biram Diouf went from Molde to Manchester United. I think he earned a lot of respect and he has become a more established player performing at a higher level. The move worked for him so why not?"
However, should a move fail to materialise Fosdahl insists that Annan would be more than happy to remain at Rosenborg.
"He is focused and committed to Rosenborg at the moment and very patient. At the moment a move could happen this week, or at the end of August. We will have to wait and see."
The Red Devils' boss Sir Alex Ferguson is looking to strengthen his midfield options following another injury setback to Owen Hargreaves, with Anderson also sidelined and both Ryan Giggs and Paul Scholes in the twilight years of their careers.
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