Adams hopes to wrap up the double swoop ahead of Saturday's game against St Johnstone, provided international clearance materialises in time.
Johansen, who is set to join on loan, will battle for the goalkeeper's jersey with Michael Fraser, who has started the last four games after ousting Mark Brown.
Left-back Ikonomou joined County last January and played 18 times before returning to his homeland in the summer to join Super League side Veria.
Adams, who is planning for a New Year's Day Highland derby, said: "We are working on a few things for the St Johnstone game.
"We are just waiting on international clearance for Eirik Johansen, a goalkeeper from Manchester City.
"And we are waiting on international clearance for Ikonomou, who was with us last season. He has been training with us for a few days.
"He's a player that did well for us last season and hopefully he can do the same again. He's 26-years-old and he's a good, solid defender.
"It gives us competition in that area. We have got Ben Gordon, who did well on Sunday against Aberdeen but Ben can play further forward as well so that gives us options on the left-hand side."
Adams has admitted that he was keen to get busy in the transfer window as he looks to spark an upturn in his side's fortunes.
They have won just three times in 18 league games - and are currently on a six-match losing streak - and would be bottom of the table but for Hearts 15-point deduction for their financial indiscretions.