Inter now look set to step up their interest although general manager Ernesto Paolillo admits they will only want him for the right price.
Paolillo, Inter's representative at the European Clubs Association conference in Switzerland, told Sky Sports News: "I am here, I am not following the market at the moment but Lampard is one, just one, of our targets.
"If he comes he will be welcome.
"Of course it is always a question between quality and price. If it is not possible to reach Lampard we will try something else."
Asked if Inter had made an offer yet, Paolillo replied: "I have been in Geneva since yesterday so I don't know the latest development."