The 23-year old Irish striker, who has a year left to run on his contract, is reportedly being targeted by Russian club Lokomotiv Moscow but even if that is only speculation, Hoops boss Neil Lennon is keen to tie him up as soon as possible.
"I've not heard a thing about other clubs being interested. He had a great season last year," said Lennon.
"He's still young - only 23 - even though he's been around the British game for what seems a lot longer.
"He's had a good season last year but there is scope for him to improve.
"He's a goalscorer and I wouldn't be in too big a hurry to let him go.
"He's in the last year of his contract and that's something we'll be looking at over the next few weeks once we get back and talk things through.
"Every player has his price and Anthony would be no different in that regard but 21 goals last year speaks for itself."