Press Association Sport understands that a number of Barclays Premier League clubs, including the Swans and Everton, have declared their interest in the 19-year-old who only joined United from Queen's Park last summer and who subsequently signed a new three-year deal last October.
However, Robertson's representative Liam O'Donnell says the Scotland Under-21 player is "perfectly happy" learning his trade on Tayside under Jackie McNamara.
Pro Legal Group lawyer O'Donnell told Press Association Sport: "A number of EPL clubs have been in contact regarding Andy.
"However, he will ignore the speculation and focus on continuing his development at Dundee United. He is perfectly happy at United ."
Everton manager Roberto Martinez was at Tannadice on Sunday to watch United's 2-2 Scottish Premiership draw with Hibernian.
It was reported that the Merseyside club are set to offer around £750,000 for Robertson with Martinez willing to loan the player back to the Taysiders for the rest of the campaign before commencing his Toffees' career at the start of next season.
United manager McNamara 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.
After the Hibernian match he said: ''It's part of the game these days. 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."