However, the Frenchman concedes that any team would one day like to hire the seven-time world champion.
This week, it was suggested that Ferrari was considering a bid offer for Hamilton, on the back of stories that Charles Leclerc might move to Mercedes.
Vasseur has a good relationship with Hamilton, having run him in F3 and GP2, and they have remained in contact over the years.
"As a joke, I could say that two weeks ago, you send [Carlos] Sainz to Audi, one week ago you send Leclerc to Mercedes,” said Vasseur when asked about the Hamilton rumours.
“Now I'm alone! You know perfectly that at this stage of the season, you will have each week a different story. And we are not sending an offer to Lewis Hamilton. We didn't do it.
"We didn't have discussions. I think every single team on the grid would like to have Hamilton at one stage, it would be bullshit to not say something like this.
“And if I discussed with Hamilton, the last 20 years, I discussed almost every single weekend with Hamilton. I don't want to have to stop to discuss with him because you're chasing me!"
Source: Autosport