A former Russian international, Zygmantovich has coached Belarussian side MTZ Ripo and is now assisting at Kaunas, both clubs with strong connections with Hearts owner Vladimir Romanov.
Frail took charge of team matters in January after Anatoly Korobochka returned to his role as director of football at Tynecastle.
But he could only steer Hearts to a disappointing eighth-placed finish in the SPL.
Korobochka and Frail had been co-managing the side following the departure of Valdas Ivanauskas in March 2007.
Weiss held talks with the Edinburgh club two weeks ago and told BBC Sport: "It would be an honour to manage Hearts.
"I'm very interested as the Scottish league would be a step up from the Slovakian league."
However, the lure of international management may keep Weiss in his homeland.
Slovakia have been drawn in a World Cup qualifying group with Czech Republic, Poland, Northern Ireland, Slovenia and San Marino.
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