The Parkhead outfit lodged a £3.5m bid for FC Schalke’s Pukki on Friday with negotiations understood to be ongoing with Werder Bremen’s Arnautovic also a target.
Reports this morning suggest a bid of around £3.5m was agreed between the two clubs for Arnautovic however the player rejected the move.
Celtic accepted a fee of around £5.5m for Hooper from Norwich City this summer.
Parkhead manager says that it would be unlikely that the club would sign both Arnautovic and Pukki.
He said: “I can confirm the interest but not that there has been a bid. I wouldn’t have thought so, not for that money anyway.
“It would be one or the other. They are two different types of players and they are both players that we like.
“I have not spoken to Peter Lawwell so I don’t know if there has been progress of Pukki, but we have made offers for him.
“At the minute they are not prepared to sell, but there might be a bit of give and take. Whether we go again for him or the others we are interested in we will wait and see.”