The Scottish champions, who face Red Bull Salzburg this evening, were quick to deny allegations, and Deila has backed Tonev to succeed following his loan move from Aston Villa.
"That has been no trouble for him," the Norwegian is quoted as saying by the Daily Mail. "We made a statement and I trust my players. I know he didn't do it.
"He is an honest player and I believe in what he is saying. He has not wasted any energy on that at all. He seems very comfortable. We are in a good mood with the whole squad and it is nothing we have used energy on.
"Aleksandar needs games. He hasn't played for a long, long time and that's the problem with a lot of the players we have. They have been in and out for a while. But he is mentally good."