The Terrors pair could join Stuart Armstrong and Gary Mackay-Steven in switching Tannadice for Parkhead.
Celtic have already begun planning for next season, with a raid on Dundee United again being mooted.
The club snapped up Gary Mackay-Steven and Stuart Armstrong from Tannadice in the winter transfer window and have recently been linked with another pair of the club's best players.
The pair are two of the Terrors best players and Celtic are once again hoping to raid the club this transfer window.
Yesterday however their boss at Tannadice, former Celtic player Jackie McNamara, implored them to remain with the club. He is quoted by the Daily Record as stating:
“Hopefully they will agree to extend because it would benefit both to be here at least another year with us.
“John has played just under 60 games and he’d benefit from playing about the same amount as Gary Mackay-Steven and Stuart Armstrong did before he leaves.
“You can see him growing into that midfield role and how good he is but he’s only 18.
“And with Nadir, again, I think another year with us would do him the world of good. You can see how hard we’ve worked with him in two years but he is influential for us and the success of the club.”
The two have been in great form in recent weeks which has seen them linked with several different moves.
Celtic are however looking to strengthen their grip of supremacy on the Scottish Premiership and a move for the pair would certainly shore things up.
Celtic are also believed to be chasing Mitchell Dijks of Willem II and Ahmad Benali of Brescia, whilst John Guidetti is expected to leave the club as his loan spell from Manchester City comes to an end.