Eugenijus Riabovas still believes he will become Hearts' new interim head coach, despite confusion over his position after his return to Lithuania.
Ivanauskas and Riabovas could be set for a job swap
But the former Kaunas coach is telling the media in his homeland that he has been given a six-month trial and will return on 1 December.
"He says his reign at Hearts will be about half a year," journalist Mindaugas Augutis told BBC Scotland.
"It is like a trial period, he may then be given a longer contract."
Augutis added that there is the possibility that current Hearts head coach Valdas Ivanauskas may be in line to take over at Kaunas should Riabovas' move go through.
"We can't reach Ivanauskas because he won't answer his phone but we believe he is somewhere in Kaunas," he added.
"There is a suggestion that he may take control at Kaunas but he may return to Hearts, not as head coach but somewhere on the coaching staff."
Hearts have insisted that Riabovas had not been due to start work this week.
"We said that he would be here before the end of the month and we have still got nine days or so to go," they said.
"We did not say that Riabovas was starting on Monday."
Riabovas had suggested last week that he would be taking over from Eduard Malofeev as temporary head coach on Monday.
Malofeev this month received a two-match touchline suspension and Hearts subsequently said that he would be leaving anyway "to progress with the attainment of his Uefa pro licence".
The former Belarus boss had taken over after Ivanauskas was given time off on grounds of ill-health in October.
So Hearts turned to Riabovas, who has led Kaunas, the club sponsored by Hearts owner Vladimir Romanov, to the Lithuanian league title.
Riabovas, who would be third former Kaunas boss to take charge of Hearts in a row, would become Hearts' seventh boss in two years.
Sunday's 1-0 defeat by Rangers led to angry protests from fans not only unhappy at the result but at the treatment of captain Steven Pressley.
The Scotland defender was out of the team for the second match in succession after speaking out against owner Vladimir Romanov's running of the Scottish Premier League club.