Baxter has been in charge of Finland for two years
Celtic are speaking to Finland coach Stuart Baxter about a possible director of football role at Parkhead.
The 56-year-old has managed several Scandinavian clubs and has worked with teams in Japan and Portugal.
The Englishman also has international experience with South Africa and took the Finland job two years ago.
Celtic are offering the role on a part-time basis but a spokesman for the Finnish FA told BBC Scotland there was no chance of a job-share for Baxter.
The spokesman also said that Baxter, who was raised in Scotland, was presently in South Africa and that the Finns did not expect to lose their manager.
Under Baxter's stewardship, Finland, ranked 52 in the world, finished third, behind Germany and Russia, in their qualifying section for this year's World Cup.
And the Finns have been drawn with Holland, Sweden and Hungary in a tough qualifying group for Euro 2012.
Baxter, who was also England Under-19s coach during Sven-Goran Eriksson's reign, was linked with Celtic 12 years ago, following the departure of then manager Tommy Burns.
Celtic aim to make Neil Lennon their new manager but are keen on the 38-year-old former captain having an older head to work alongside.
Lennon was in charge of the Under-19 side at Celtic Park before taking over from the sacked Tony Mowbray in March.
Despite his lack of experience, Lennon won all eight of the league games he oversaw as Celtic put in a strong finish to a disappointing season without silverware.
And Lennon is expected to have the final say on a future football director, if he gets the job.
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