Germany's Auto Motor und Sport claims the day after the German grand prix was a crucial one for Force India, amid obvious financial problems.
"There is mounting speculation that Force India will file for bankruptcy," said correspondent Michael Schmidt.
Another German publication, Auto Bild, says fashion mogul Stroll could be the saviour.
"It is unclear whether he has secured a majority stake or if the team now belongs completely to him," said correspondent Ralf Bach.
Other parties have also looked into buying Force India recently, including major sponsor BWT and the British energy drink Rich Energy.
"People have been writing about the ownership of my team for years," team boss Vijay Mallya said earlier in July.
"You will not see anybody in Force India walking around with a For Sale sign. All I can say is if there is a credible offer with cash on the table, I will be the first to discuss with my shareholders.
"Until then, speculation remains speculation," he added.