The German forward swapped London clubs in the summer, while Cucurella ended up staying at Stamford Bridge.
Havertz starred for Germany in a 3-2 loss against Turkey, playing in Cucurella's usual left-back slot.
After the game, Cucurella posted "LB (fire emoji)" on the Instagram account of Havertz.
The Spaniard does not appear to be threatened by his German colleague impressing in his position.
Havertz, who plays as a midfielder or forward for Arsenal, moved for £65 million this summer.