Weiss has a good record with Artmedia Bratislava
Artmedia Bratislava coach Vladimir Weiss says he is to hold further talks at the weekend with Hearts about their vacant managerial position.
Weiss guided his club to a league and cup double last season and is high on Hearts' list of candidates, along with Icelander Gudjorn Thordarson.
"It would be an honour to manage Hearts," Weiss told BBC Scotland.
"I'm very interested as the Scottish league would be a step up from the Slovakian league."
The former Czecheslovakia international is in his second spell as boss of Artmedia.
Scottish fans may remember him from the 2005 Champions League.
First, he engineered Celtic's exit from the qualifying stages with a 5-4 aggregate win.
There hasn't been an approach at all
IA Akranes chief executive Toddy Gudjonsson
And, in the group stage, he returned to Glasgow to face Rangers.
After a 12-month spell in Russia with FC Saturn, he returned to Bratislava at the start of last term.
Artmedia have admitted that they are aware of Hearts' interest in the 43-year-old.
But IA Akranes insist that there had been no approach for their coach, former Stoke City boss Thordarson.
Akranes chief executive Toddy Gudjonsson, who is also Thordarson's son, told PA Sport: "Of course we heard about this in the winter.
"However, we haven't heard anything about this since and there hasn't been an approach at all. This is the first I've heard of it again."
Thordarson previously spent three years in charge of Stoke from 1999, and also had short spells as manager at Barnsley and Notts County, where he won just 13 of his 50 matches in charge.
Should the 52-year-old take charge at Tynecastle, former Motherwell manager Terry Butcher, who is presently one of George Burley's assistants with Scotland, could be his deputy.
Hearts announced in January that they were on the lookout for a new manager.
Stephen Frail took charge of the team for most of last season after Anatoly Korobochka returned to his role as director of football.
Frail remains caretaker manager but has admitted that he does not expect to be given the job permanently.
The Tynecastle club had been hoping to bring in Mark McGhee as their new manager, but he decided to remain with Motherwell.
Since Lithuanian businessman Vladimir Romanov bought a majority stake in the club in 2005, John Robertson, George Burley, Graham Rix and Valdas Ivanauskas have all come and gone as manager.