The Finn, who plays for Schalke in Germany, is expected to finally complete a move to Glasgow this week, with Neil Lennon’s side in desperate need of player recruitment.
Pukki is ready to agree terms and move to Parkhead if Celtic can meet “concrete pre-arranged conditions”, although he won’t be eligible for this week’s Champions League showdown with Shakhter Karagandy.
The 23-year-old has been told he can leave the Bundesliga side. His agent Gerrit Gertung confirmed last night Celtic had been in again for Pukki and are ahead of other clubs in the race for the former Sevilla forward.
Gertung said: “The offer has been rejected by Schalke, but there is still time until the end of the transfer window, so that is not an issue.
“There are concrete pre-arranged conditions that have to be met, then to my knowledge Pukki should leave Schalke.
“There have been other enquiries made, but none in the form that can be considered actual bids. They are not enough that would influence the parties involved.”
Pukki has played just 17 minutes of football for Schalke this season and was an unused substitute in the weekend defeat by Hannover.
He will be Lennon’s fifth signing this summer after landing Amido Balde from Vitoria Guimaraes, Virgil van Dijk from FC Groningen, Wolves defender Steven Mouyokolo and Ajax’s Derk Boerrigter.
Perhaps of more immediate concern to Lennon is Wednesday night’s Champions League play-off return leg against Karagandy in which Celtic must try to overturn a 2-0 deficit.
The manager will spend today checking on the fitness of his squad following Saturday’s 2-2 Premiership draw with Inverness Caledonian Thistle.
Georgios Samaras and Kris Commons are most likely to recover from injury ahead of the European match, with winger James Forrest and summer recruit Boerrigter rated 50-50.
Anthony Stokes is a doubt and Beram Kayal has all but been ruled out of the return leg after a groin strain forced him out of the Inverness game.