Kokinis, the leading candidate to take over as the Browns' GM, spoke with team owner Randy Lerner on Wednesday and could be days away from joining the club.
It isn't known if Lerner offered Kokinis a contract, but the 41-year-old's hiring seems inevitable.
Kokinis spent Monday and Tuesday at the Browns' headquarters in Berea meeting with Mangini and other members of Cleveland's coaching staff.
"We talked through every different issue that we could think of collectively, and it was nice to be able to have that time to do that and over a very concentrated space -- just the two of us," Mangini said at the Greater Cleveland Sports Awards.
While presenting an award, Mangini, who began his NFL career as a public-relations intern with Cleveland, told the audience he anticipated the Browns "will have news in the very short future."
Pressed later on Kokinis' probable arrival, Mangini said the Browns were being thorough before naming their top football executive.
"The way that we've done this is that we've had different meetings, and in terms of when and where, there's been a bunch of them," Mangini said. "Randy and I have been talking a lot, and we're trying to move forward with the decision as quickly as we can. But it's definitely a process, and we're not going to rush the process."
Lerner, who initially interviewed Kokinis on Jan. 11, wasn't involved in the meetings earlier this week.
Mangini hired his offensive and defensive coordinators last week and is expected to announce other assistant-coaching hires Thursday.
Copyright 2009 by The Associated Press