Robertson is in talks with Hull after the two clubs agreed a fee reported to be £3m for the 20-year-old Scotland international.
The 20-year-old full-back, who only became a professional last year after joining the Tannadice club from Queen's Park, has attracted interest from a number of other Premier League clubs with West Ham and West Brom reported to be keeping tabs on him.
The player's representative, PFA Scotland lawyer Liam O'Donnell, said: "Andy is in talks with Hull.
"Clearly, it's a massive decision for him and he will carefully consider all the aspects of this potential move.
"The most important of these is to try to continue the excellent progress he has made these past 18 months."
United boss Jackie McNamara admits he is hoping for a shock U-turn.
"The two clubs have agreed a fee so we’ll find out in the next couple of days whether it’s either a 'yes' or a 'no' and hopefully it’s a 'no'," he told the Daily Record.
"We’ll wait and see. It’s all down to Andrew and his family, the decision he makes. He’s got to speak about personal terms, his future.
"Selfishly, I hope he decides to stay another year but sometimes these things are out of your control."