The Dnevni Avaz daily quoted unnamed sources as saying that another two potential candidates, French Alain Le Roy and Italian Stefano Santorino, seemed to have jettisoned plans to be engaged in Bosnia.
Lajcak, currently a director within the Slovak Foreign Ministry, has won a reputation of being an expert for the situation in the Balkans.
He was credited for successful mediation in talks for the preparation of Montenegro's independence referendum in 2006.
The term in office of the current High Representative, German Christian Schwarz-Schilling, expires on 1 July.
The Peace Implementation Council is expected to name his successsor until the end of May.