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!"
Asked if he’d had to reassure his current drivers about the Hamilton rumours, Vasseur again laughed it off.
“They didn't have to reassure me last week when you sent them to Sauber, or for Charles to Mercedes!,” he said.
“They didn't come to see me and say 'Fred, don't worry, it's not true.' We are used to it, and we know that each week we will have a new rumour, and we are just focused on the job.”
Vasseur insisted there was no hurry to extend the current deals of either Leclerc or Sainz.
"No, because as I told you last week or two weeks ago that the most important thing for us is to stay focused on the development and the current season.
"In a couple of months, we'll have the discussion about the future, and it will be time to discuss.
“I didn't want to discuss with them the extension, and I didn't change. I told my position, that the most important thing is to try to do a step forward to be able to compete with Red Bull and let's stay focussed on this."
He added: "For us, we agreed that we'll discuss about the contract later on and I don't want to change, because we had the rumours from someone that Lewis could come or Charles could go, or Carlos could go. We are doing our job internally, and I will stay focused on the plan."
