The former Netherlands international is keen on a move to the Scottish champions, having been shown the door by Middlesbrough's new manager, Gareth Southgate.
The Celtic manager, Gordon Strachan, thinks that the former Chelsea man, even at 34, can replace the departed John Hartson. But Hasselbaink's agent, Humphry Nijman, will know in the next 24 hours whether the Glasgow club can afford the player's reported £40,000-a-week salary.
Nijman said: "Celtic have shown an interest and now we are speaking further. If a club wants a player and if the player wants to go, then we start to talk. He thinks Celtic are very interesting, a fantastic club with a great stadium and supporters.
"We all know Celtic are one of the biggest clubs in the world and now we will be speaking to see if a move is possible, but we haven't reached an agreement.
"They have to make clear whether they are in a position to sign him. There are three Premier League teams in for him so we have to find out one way or the other. Hopefully, a decision will be made by tomorrow."
Celtic, who are away on tour in Poland, have also been linked with a swap deal involving the Bulgarian midfielder Stilian Petrov, who wants to leave and Manchester City's Joey Barton.Reuse content