Sky reports that the two sides have agreed on a collaboration in principle, and that a successful conclusion to the talks is expected soon.
Sporting director Rouven Schröder had already confirmed on Saturday that Gladbach had reached an agreement with one candidate, without naming him, according to Fussballtransfers.
Blessin had been linked with the Foals alongside two other names in recent days. Enrico Maaßen, currently at FC St. Gallen, and the club-less Vladimir Petković were also mentioned as possible successors to Polanski.
Borussia Monchengladbach have been searching for a new coach since Polanski’s dismissal.
Blessin's last job was with St Pauli, having been dismissed over the summer after their relegation last season from the Bundesliga.
The German spent two years with St Pauli and also has past Serie A experience with Genoa.