The Serie A club had themselves identified the experienced Vertonghen as a possible replacement for Chris Smalling, whose loan deal from Manchester United expires this summer and they may not be able to finance a permanent transfer.
It is said they turned to Vertonghen, who is now a free agent after his contract at Spurs expired and were told they face interest from Atleti.
Renan Lodi is the only specialist left-back in Diego Simeone’s first-team squad and Vertonghen is comfortable in that position, alongside in the heart of defence.
Having been capped 118 times at international level for Belgium, Vertonghen made 315 first-team appearances for Spurs spread over eight seasons but has now left North London.
A separate report from German outlet Kicker is cited by Diario AS as claiming that Borussia Monchengladbach defender Matias Ginter is also being tracked by Atleti this summer, as they aim to bolster their defensive options next season.