Final interviews have taken place and the Easter Road board will discuss the merits of both candidates this week before making a decision on who should take charge of the team for the 2022/23 campaign and beyond.
Former Sunderland and Bristol City boss Johnson appeared to be the frontrunner for the role, but Tomasson emerged as a contender late last week and is now set for a shoot-out with Johnson for the vacancy after both impressed the Hibs hierarchy.
Speaking last month, the former Denmark internationalist said his plan was to seek a return to management in the summer.
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He told TV 2 SPORT: “It must be the right project. It doesn’t have to be a top team; if the project is interesting and the club is going in an interesting direction, it can also be really, really exciting."
Club chiefs have said since the start of the process that they would not be rushed into an appointment following the sacking of Shaun Maloney in mid-April, just 120 days into his reign as manager, after a disappointing run of results and failure to finish in the top six of the Scottish Premiership.
Former Lincoln City boss Michael Appleton, who was strongly tipped to succeed Neil Lennon at the Capital club in 2019, made the shortlist of candidates along with Johnson and Tomasson but appears to be out of the running.