A number of Barclays Premier League clubs, including Swansea and Everton, are reportedly interested in the 19-year-old, who only joined United from Queen's Park last summer and signed a new three-year deal in October.
However, Liam O'Connell, Robertson's representative, says the Scotland under-21 player is "perfectly happy" to continue to learn his trade on Tayside under Jackie McNamara.
"A number of English Premier League clubs have been in contact regarding Andy," O'Connell said. "However, he will ignore the speculation and focus on continuing his development at Dundee United. He is perfectly happy at United."
Roberto Martinez, the Everton manager, was at Tannadice on Sunday to watch United's 2-2 SPFL Premiership draw with Hibernian.
It was reported that the Merseyside club are likely to offer around £750,000 for Robertson with Martinez willing to loan the player back to the United for the rest of the campaign before commencing his Barclays Premier League career next season.
McNamara also has several other young stars including Ryan Gauld and John Souttar subject to speculation about their future. The former Celtic and Scotland defender, however, continues to stress his desire to keep his young players at the club and has admitted he will be happy when the transfer window closes at the end of the month.
"It's part of the game these days," he said. "You can't get away from it. I'll be happy when the window shuts. As far as I'm concerned, it's important that we keep them all so they can continue to learn their trade here."
McNamara also praised the contribution of striker Brian Graham, who rescued a point for United on Sunday, coming off the bench to score a last-gasp equaliser against Hibs.
"Brian deserves a lot of credit, as he's had to be patient since he came here," he said. "But he showed what he was capable of on Sunday."