The German club's keeper is carrying a clause in his contract that allows Bundesliga top-five clubs to sign him for between €10 million and €15 million — though Premier League teams would pay a fixed fee of €15 million.
Martínez's future at Villa Park has been uncertain since the Argentine came close to joining Manchester United last summer. The 33-year-old remains under contract at Villa but has expressed a desire for a new challenge at a club competing for the highest honours, and Unai Emery's side — despite a successful Europa League triumph — have not been able to offer Champions League football next season.
Nicolas, 27, kept 13 clean sheets in 34 Bundesliga appearances this season, playing a significant role in Borussia Monchengladbach's push for Europa League qualification under head coach Eugen Polanski.
Polanski offered an emphatic assessment of his goalkeeper's quality after a standout individual display in a 1-0 defeat to RB Leipzig.
"The fact that Mo was voted man of the match despite the fact that we lost speaks volumes. Such a performance doesn't surprise me. It's a manifestation of what he delivers week after week and day after day in training. He's an excellent keeper."
Nicolas is left-footed — an unusual characteristic for a goalkeeper that has drawn comparisons with Marc-André ter Stegen — and distributes well to Villa's high defensive line.
Aston Villa have not made a formal approach and are assessing the situation as part of their summer planning. Whether Martínez pushes for a move this summer will determine whether the interest in Nicolas advances into something more concrete.