Johansen, who is set to join on loan, is listed in City’s elite development squad.
The 21-year-old Norwegian, who is 6ft 4in tall and has trained with his national team, went out on loan to Scunthorpe United last season.
He will battle for the goalkeeper’s jersey in Dingwall with Michael Fraser, who has started the last four games after ousting Adams’ previous first choice, Mark Brown.
Left-back Ikonomou joined County last January and played 18 games with the Dingwall side, losing just four times, before returning to his homeland in the summer to join Super League side Veria.
Adams, whose team host St Johnstone on Saturday after their New Year’s Day derby against Inverness, said: “We are working on a few things for the St Johnstone game.
“We are just waiting on international clearance for Johansen and for Ikonomou, who 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.”
Adams, whose team sit in the Premiership play-off slot, added: “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.”