The 23-year-old Finland international has travelled to Glasgow to discuss personal terms and complete a medical after the SPL champions upped their initial offer of £850,000
Schalke striker Teemu Pukki is set to join Celtic in a deal worth €2.5 million (£2.1m), Goal understands.
The 23-year-old's contract at the Bundesliga side is set to expire at the end of the season, with the SPL champions initially seeing an opening offer of €1m rejected (£850,000).
Pukki has now travelled to Glasgow to discuss personal terms and complete a medical.
Pukki's agent told Goal: "He will be in Scotland to clarify the last details tonight. We expect the transfer to be completed afterwards."
Celtic confirmed their passage to the Champions League group stage on Wednesday with a 3-2 aggregate win over Shakhtar Karagandy, and manager Neil Lennon is confident the lure of the competition will be key to recruiting players.
"We have agreed a fee for Pukki but haven’t agreed personal terms," Lennon told reporters.
"I think the carrot of the Champions League might be a bigger draw for a lot of players. It puts us in an excellent position."
Schalke 04 are expected to use the funds from Pukki's sale to sign a replacement striker.