The Scottish side wants to bring in Keane on loan, as they can not afford to buy the Spurs striker.
Mjallby told the Daily Record: “Has Neil been speaking to Robbie? Definitely.
“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.”
He added: “To buy someone at Robbie’s level would be impossible. We don’t have that kind of money.
“The only way we could get that kind of player would be to ride our luck and maybe find someone on loan and make sure it’s a quality player who is going to give us goals.
“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.”