The Hoops believe they have already overcome several significant obstacles to put in place a loan deal for the Ghanaian wide midfielder, whose current club, Russia's Rubin Kazan, are looking to sell at a price of around £5million.
But Celtic want to see how the 24-year-old former Espanyol and Villarreal player settles here, and will sign Wakaso on a year-long loan with an option to buy.
However, they face a huge challenge to get everything in place before Uefa's 11pm deadline for the one extra player they can still add to their squad for the Champions League play-off ties.
To expedite proceedings, Wakaso will have a medical in Russia today then fly straight to Slovenia to meet up with his new team-mates and manager Ronny Deila. Celtic have to complete all the formalities required for Wakaso to be registered with the SFA before Uefa's deadline.
That includes receiving international clearance from Russia, and a work permit for the man who has played 19 times for Ghana, scoring seven goals.
Celtic believe they will be granted this final piece of paperwork without the need to take the case to appeal.
The man who played for Ghana at this summer's World Cup finals in Brazil will become the fourth player to join the club on loan, following Jo Inge Berget, Aleksander Tonev and Jason Denayer.
Of this quartet, only Manchester City wonder kid, Denayer, has not arrived with an option to buy.
Deila initially stated he is not a fan of loan signings as he did not see the point of developing players for other clubs.
But, he has since qualified that by saying it is the best approach at the moment while he assesses what he has, what he needs, and what is available.
Since returning from Brazil, Wakaso has been playing for Rubin in the Russian league and is match fit and ready to go straight into action if all the boxes can be ticked by tonight's deadline.
His pace and power are what has convinced Celtic it is worth trying to overcome all the difficulties surrounding his signing at such a late hour.
The next registration deadline for inclusion in Group Stage games in either the Champions League or Europa League is September 2.
So, even if Celtic can't get Wakaso's paperwork completed in time for him to be eligible for this round, they will still proceed with the loan signing.
Success against Maribor would guarantee them at least £15m for reaching the Champions League, and make the final few days of the transfer window a flurry of activity in terms of transfer business.
Celtic mean to make the most of the opportunity after the Court of Arbitration for Sport yesterday refused to grant Legia Warsaw's request to have overturned Uefa's judgement that the Polish side fielded an ineligible player in the second leg of their qualifying tie against the Hoops.
CAS also refused to accede to Legia's request to for 'provisional measures' to be implemented to force the postponement of Celtic's tie against Maribor and the Plish club's Europa league Play-off against Aktobe.
Legia's outspoken co-owner, Dariusz Mioduski admitted: "Knowing both Uefa and Celtic would be filing documents and arguing against us, we didn't expect the courts would make a different decision at this point.
"But we will not give up on our pursuit on what we believe is justice for football."
The case will now be heard by CAS at a full hearing, but this will not be convened for a number of weeks.
The news came as a huge relief - but not a surprise - to Celtic.
Not so heartening is the fact the referee for tomorrow's match in Maribor is Pavel Kralovec.
The Czech Republic official was in charge when Celtic crashed 2-0 to Shakhter Karagandy in Kazakhstan at the Play-off stage of the competition last season.