The midfielder plays for Israeli club Bnei Yehuda and said his farewells to his team-mates after playing in a cup tie on Wednesday against Hapoel Afula.
But the deal with Celtic was placed in jeopardy when Soro's agents wanted a bigger chunk of the fee because they insisted they owned a percentage of the player, which was disputed by Bnei Yehuda.
The dispute now looks to have been resolved and Soro told Israeli journalists: "I will leave on Friday to fly to Glasgow."
If the deal goes through he will become Celtic manager Neil Lennon's second major signing of the transfer window after the £3.4 million capture of Polish striker Patryk Klimala.
Soro's manager at Bnei Yehuda, Elisha Levy, has already started the hunt to replace the midfielder.
He said: "We already know Ismaila is leaving so that makes it important for us to find his replacement. It's never easy to find a replacement for a player of his quality in January."