The 18-year-old has had a breakthrough campaign under Stephen Glass after making his debut towards the end of last season.
Ramsay recently returned to the team after an injury lay-off which followed an excellent start to the season when he was the Dons’ best player.
His promise has attracted admirers from down south and three English sides have been linked with a January move for the right-back.
The Daily Record report Leicester City are weighing up an approach.
But the Scottish Sun suggest Watford are the first to make contact with Aberdeen while Newcastle United also track Ramsay as Eddie Howe looks to reshape his squad with the club 19th in the Premier League.
Speaking earlier this month, Dons chairman Dave Cormack noted how much they value their academy product.
“There are not many right back at his age like him, doing what he does,” he said.
“Look at the data and all the clubs look at the same (scouting) systems. He is in the elite upper bracket, right up there, for a young right-back in Europe.”
Ramsay, who made his Scotland Under-21 bow against Turkey earlier this season, has demonstrated his ability on the ball and as an attacking outlet for Aberdeen, while possessing an aggressive and determined defensive approach.
Of all teenagers to play in the Premiership this season no player has contributed to more goals than Ramsay’s four with only Hibs defender Josh Doig playing more minutes.