The Swiss squad have struggled to stay above water since parting with BMW in late 2009 and face particular problems this year having not yet registered a single World Championship point.
That leaves them 10th in the constructors' standings and thus in danger of losing significant prize money, making their financial situation all the more perilous.
During the Italian Grand Prix weekend Stroll was mooted by German media reports as potential buyer for the team. The Canadian-born businessman made his fortune in clothing retail, notably with the Tommy Hilfiger brand and fashion house Michael Kors, and now resides in Geneva.
Stroll already has strong links to motor racing, too. He owns the Mont Tremblant circuit is his native Canada, while his 15-year-old son Lance is a successful former karter who has this year stepped up to single-seaters and currently leads the Italian F4 Championship. Stroll was also linked with making an investment in F1 earlier this year.