The club's majority shareholder Vladimir Romanov has reportedly narrowed his search to three names - former Stoke boss Gudjon Thordarson and Belarussian Andrei Zygmantovich being the others - and has already held talks with Weiss, according to the 43-year-old Slovakian.
Weiss, who coached Artmedia to a famous 5-0 win over Celtic in a Champions League qualifier in 2005 before drawing twice with Rangers in the group stage of the competition, told the Edinburgh Evening News: "I don't want to talk about my contract. I have had some discussions already.
"What can I say? This weekend I have a meeting with Hearts so maybe I will know more next week.
"I know everything about Hearts and it is a very exciting chance for me, but this is my business and I must do it privately. It's my problem."