Midfielder Yosuke Ideguchi, the versatile Reo Hatate and forward Daizen Maeda are the three in question as Ange Postecoglou taps into a market he knows well from his time as Yokohama F. Marinos boss.
Kyogo Furuhashi has been a revelation since joining in the summer, becoming a key man at Parkhead with 16 goals in 26 games.
Ideguchi and Maeda are the closest to joining him in Glasgow with the duo having travelled to undergo medicals ahead of the switch.
According to reports in Japan, contracts are all but agreed and a "press conference will be held soon”.
Maeda, who played under Postecoglou at Yokohama, will initially join on loan with a view to a €2million transfer in the summer, while Ideguchi, who signed for Leeds United for £500,000 in 2018, will join for just over €1million from Gamba Osaka.
While Hatate is expected to depart Japan at the beginning of January.
The Kawasaki Frontale star can play a variety of roles, including left-back, left-wing and in the centre of midfield.
Postecoglou is being cautious about putting time scales on new signings due to Covid-19 as he tries to do his transfer work early.
“I’m always optimistic but the world flies in the face of it sometimes. We’ve just got to do what we do,” he said.
“That’s why I’m reticent to say, ‘yes definitely in this time frame [new players will be in]’, because things change on a daily basis at the moment with the way the world is."