The 30-year-old spent nine years with the Amsterdam-based side before joining Spurs in July 2012 and his mum, Ria Mattheeuws, is keen to see him return to his former stomping ground.
She told news outlet 'HLN': 'I hope that he can remain healthy and injury-free, so that he can go further on this level, and if he can not, maybe at a lower level.
'It would be nice if he could go back to Ajax, but if he doesn't compete with Tottenham, why would Ajax succeed? With the national team I hope for a World Cup final in Russia, or world champion.'
Vertonghen is unlikely to be in a rush to return to his former club though, having established himself as one of the Premier League's top defenders and helped Spurs to become genuine title challengers.
The Belgian is currently away with his national side and could become his country's all-time record appearance maker if he gets on the pitch in Belgium's final two World Cup qualifiers.
Vertonghen is under contract with Spurs until 2019.