The younger Lukaku has a similarly intimidating build to his brother but actually plays as a left-back as opposed to a striker.
Jordan, 19, is owned by Anderlecht but is currently playing on loan at KV Oostende in Belgium's top division.
Jordan has nine caps for the Belgium U21 side and it is believed that Spurs watched him play for the U21 national team against Italy on Monday night.
Italian giants AC Milan have also being linked with Jordan.
Jordan's brother Romelu, 20, has got off to a fine start to the season on loan at Everton.
When Romelu signed for Chelsea he admitted he hoped his brother could join him some day.
"I have loved Chelsea since I was a boy. Now that I have fulfilled a dream by joining Chelsea, my final one is to have my brother join my one day," Lukaku said on signing.
"It's our dream to lay in the same team. We have done it in friendly games but, one day, we hope to do it when it matters.
"Technically he is better than me. He is a left winger who is very skilful and strong. I think when the scouts see him, they will see what he can do."
However, as yet, there is no indication that Chelsea are keen on Jordan.