The 20-year-old established himself last season as an important member of the Hearts first team.
Championship side Burnley, bossed by former St Johnstone manager Owen Coyle, are among several teams to have sent scouts to watch him.
However Hearts are refusing to sell at the current price being offered by Burnley, which is reportedly in excess of %uFFFD500,000.
Clarets assistant boss Sandy Stewart told the Lancashire Evening Telegraph: "We made an increased offer for Andrew this week but that has been rejected by Hearts."
Stewart admits that could spell the end of Burnley's interest.
"We'll have to wait and see," he said. "We've got other targets who may become available in the meantime."