The former Under-21 striker would be following in the footsteps of his brothers Arnar (Bolton, Dundee United and Leicester) and Bjarki (Preston) in playing for British teams.
Available for free from his club Valur, Gunnlaugsson said: "I am ready to agree to the contract and I am quite excited about the move."
Dunfermline manager Jim Leishman said: "We're watiing on word to see if he's going to come in.
"He came for a week's trial and hopefully can sign for us. This boy is just a late starter."
"We're looking to strengthen all over," said Leishman.
"We need strength in depth thoughout the squad.
"If the players are right, we're hoping we can bring some players in.
"We're looking, but it's hard getting the right ones."
Chairman Yorkston was keen to remind Pars fans to keep their feet on the ground, and keep the pressure off the player "He is keen to forward his career and sees an move to us as a way of doing that," he said.
"But we're not saying he's the answer to our striking problems."