But Celtic are hoping to be in the frame, and Spurs would rather get the Republic of Ireland striker out of the Premiership, just as Newcastle did with Craig Bellamy when Graeme Souness was at the club.
Keane is still seen as surplus to requirements at White Hart Lane with some suggesting he has fallen out Spurs manager Harry Redknapp.
Hughton still has contacts at White Hart Lane, and there would be no harm in trying to push through a deal.
Celtic assistant manager Johan Mjallby: "I don't know Tottenham's thinking when it comes to Robbie. He is out of our reach when it comes to buying him. But a loan would be perfect for us.
"To buy someone at Robbie's level would be impossible. We don't have that kind of money.
"But we have the lure of European football at Celtic. From my own memories it's very important as a player. It's a great opportunity to play against the best and develop."