Tottenham managed to record a 2-1 victory over Southampton at White Hart Lane and move to within 10 points of the Blues, who defeated Stoke 2-1 on Saturday to extend their advantage at the time.
A neat strike from Christian Eriksen and a Dele Alli penalty gave the hosts a 2-0 lead at the break before the Saints pulled one back in the second period through James Ward-Prowse.
Mauricio Pochettino's men remain in second with the win and Vertonghen has warned Chelsea his side won't be giving up anytime soon in their quest for the Premier League title.
"Chelsea are favourites for the title but we won't give up until they lift the trophy," he told Sky Sports. "We are doing well and have to aim for the highest place possible and keep winning our games."
Tottenham return to action after the international break on April 1 when they make the tricky trip to Burnley before travelling to relegation-threatened Swansea four days later.