The England international has missed the past month due to an ankle injury sustained in the 2-2 draw at home to Aston Villa, with manager Brendan Rodgers saying at the time that Johnson would miss an "indefinite" amount of time.
But Johnson is in contention to feature against Garry Monk's men at Anfield this weekend.
"Glen has been back training," Rodgers said.
"According to him, he has felt as good as he has done for a long time - which is great. He has looked very good in training and he'll come into the squad."
Midfielder Lucas Leiva and centre-back Mamadou Sakho are also nearing returns from knee and hamstring injuries respectively, but Jose Enrique has travelled to America in order to get specialist advice on his knee complaint.
Rodgers added: "Lucas Leiva is recovering very well but not in the squad.
"Sakho is still probably a week or so away, but he's back on the field now with the rehabilitation team and working well.
"Jose Enrique has been out in America. We're looking to try to put an end to his injuries this season.
"We have sent him out to get some specialist advice on that. But he's nowhere near playing yet."
Liverpool's January transfer target Yevhen Konoplyanka scored the winning goal in Dnipro's 1-0 victory over Tottenham in the Europa League on Thursday.
Rodgers was asked whether he would renew his interest in the winger in the close-season, but the Liverpool boss kept his cards close to his chest.
"We've got lots of people that were looking at," he continued.
"We'll assess where we are at the end of the season and take it from there."