Gladbach parted ways with Polanski at the weekend after a torrid start to the season that included defeats to RB Leipzig, promoted SV Elversberg and a 5-0 thrashing at SC Freiburg that left the club pointless and with 12 goals conceded from three matches. Assistant Jan-Moritz Lichte has taken interim charge while sporting director Rouven Schröder searches for a permanent successor.
Danish outlet Tipsbladet reported on Monday evening that Gladbach were preparing a multi-million-euro offer for Priske, who remains under contract at Sparta Prague, with talks expected to begin shortly.
The 49-year-old previously managed Feyenoord Rotterdam, FC Midtjylland and Royal Antwerp, giving him plenty of experience working abroad, and he memorably inflicted a 3-0 defeat on Bayern Munich with Feyenoord in the Champions League last season.
The story took a swift turn on Tuesday morning, however, with German outlets moving quickly to dampen the speculation. The Rheinische Post reported there was "nothing to" the rumour, while Sky said a deal would not be completed.
Several other names remain in the frame for the Gladbach job: Christian Eichner, most recently at Karlsruher SC; Horst Steffen, who left Werder Bremen; Alexander Blessin, formerly of St Pauli; and Bo Henriksen, who was sacked by Mainz 05. Ole Werner had reportedly already signalled he was not available for the role.
According to Bild, Schröder has around €4 million available to spend on the appointment, with the club prioritising a coach who has senior playing experience, is comfortable working under pressure and can bring immediate stability to the squad - qualities that need not necessarily come from a candidate outside Germany, though speaking German is considered important.
With the international break offering some breathing room, Borussia Monchengladbach are not expected to rush the decision, though the scale of their poor start means pressure to find the right appointment will only grow the longer the search continues.
Notably, Priske is also the father of striker August Priske, who won the Allsvenskan Golden Boot with Djurgården before moving to Birmingham City in January. Unlike most of the other candidates on Gladbach's list, Priske was not a free agent, which explains why any deal for him would have required Sparta's cooperation and a transfer fee rather than a straightforward appointment.