The Welsh defender, pictured, has been out of action since breaking a collar bone in the win over Motherwell at Parkhead on October 5.
However, he has shown enough in training over the past week to persuade Neil Lennon he should be in contention to play against Barcelona in the closing Champions League Group H match.
Matthews' biggest obstacle to such a high-profile return is the electric form of Mikael Lustig and Emilio Izaguirre.
But, Lennon wants to get the Welshman back into the side as soon as possible, and a wide midfield role could be an option.
He will join Georgios Samaras, Nir Biton and James Forrest in being added to the squad which crushed Motherwell 5-0 on Friday.
"Biton, Samaras and Matthews will be in the squad for Barcelona," confirmed Lennon.
"And Forrest, hopefully, will be fit for Wednesday."
Forrest's recovery from his hamstring problem will be assessed over the next 24 hours.
But Lennon is confident Matthews is ready to go once again and said: "Players are champing at the bit and we are getting more back now.
"Adam is there now and he will add to the squad. He's a very good player, very versatile as well.
"He was starting to hit really good form and it was a sore one for him.
"He has made a very good recovery and I'm hoping we will see him in the team in the next week or so."
Matthews' return could finally allow Izaguirre to get some much-needed rest over the next few weeks, though Lennon explained the Honduran does not want to miss out.
Along with the overlapping Lustig, Izzy was a key player in the waves of attacks which eventually swamped Motherwell at Fir Park.
But, while Lennon is delighted with the form being shown, he is conscious of how many games Izaguirre has been asked to play already this season, and how much travelling he has done to play for his country as they booked their place in the World Cup finals.
Lennon explained: "He doesn't want to be rested. There will come a time when he has to step out, but, at the minute he looks so strong.
"We do rest him in between games. But, his effervescence emanates through the whole team.
"He's back to his very, very best. He's playing brilliantly, and has done for quite a while now."
The battle for the full-back positions at Celtic will become even more competitive if the Hoops are successful in landing Partick Thistle's Aaron Taylor-Sinclair.
He is out of contract next summer and has confirmed the Parkhead club have made contact with his agent.